Tunable stiffness enables fast and efficient swimming in fish-like robots.

Fish maintain high swimming efficiencies over a wide range of speeds. A key to this achievement is their flexibility, yet even flexible robotic fish trail real fish in terms of performance. Here, we explore how fish leverage tunable flexibility by using their muscles to modulate the stiffness of their tails to achieve efficient swimming. We derived a model that explains how and why tuning stiffness affects performance. We show that to maximize efficiency, muscle tension should scale with swimming speed squared, offering a simple tuning strategy for fish-like robots. Tuning stiffness can double swimming efficiency at tuna-like frequencies and speeds (0 to 6 hertz; 0 to 2 body lengths per second). Energy savings increase with frequency, suggesting that high-frequency fish-like robots have the most to gain from tuning stiffness.

Future Tail Tales: A Forward-Looking, Integrative Perspective on Tail Research.

Synopsis Tails are a defining characteristic of chordates and show enormous diversity in function and shape. Although chordate tails share a common evolutionary and genetic-developmental origin, tails are extremely versatile in morphology and function. For example, tails can be short or long, thin or thick, and feathered or spiked, and they can be used for propulsion, communication, or balancing, and they mediate in predator-prey outcomes. Depending on the species of animal the tail is attached to, it can have extraordinarily multi-functional purposes. Despite its morphological diversity and broad functional roles, tails have not received similar scientific attention as, for example, the paired appendages such as legs or fins. This forward-looking review article is a first step toward interdisciplinary scientific synthesis in tail research. We discuss the importance of tail research in relation to five topics: (1) evolution and development, (2) regeneration, (3) functional morphology, (4) sensorimotor control, and (5) computational and physical models. Within each of these areas, we highlight areas of research and combinations of long-standing and new experimental approaches to move the field of tail research forward. To best advance a holistic understanding of tail evolution and function, it is imperative to embrace an interdisciplinary approach, re-integrating traditionally siloed fields around discussions on tail-related research.

Swimming Turned on Its Head: Stability and Maneuverability of the Shrimpfish (Aeoliscus punctulatus).

The typical orientation of a neutrally buoyant fish is with the venter down and the head pointed anteriorly with a horizontally oriented body. However, various advanced teleosts will reorient the body vertically for feeding, concealment, or prehension. The shrimpfish (Aeoliscus punctulatus) maintains a vertical orientation with the head pointed downward. This posture is maintained by use of the beating fins as the position of the center of buoyancy nearly corresponds to the center of mass. The shrimpfish swims with dorsum of the body moving anteriorly. The cross-sections of the body have a fusiform design with a rounded leading edge at the dorsum and tapering trailing edge at the venter. The median fins (dorsal, caudal, anal) are positioned along the venter of the body and are beat or used as a passive rudder to effect movement of the body in concert with active movements of pectoral fins. Burst swimming and turning maneuvers by yawing were recorded at 500 frames/s. The maximum burst speed was 2.3 body lengths/s, but when measured with respect to the body orientation, the maximum speed was 14.1 body depths/s. The maximum turning rate by yawing about the longitudinal axis was 957.5 degrees/s. Such swimming performance is in line with fishes with a typical orientation. Modification of the design of the body and position of the fins allows the shrimpfish to effectively swim in the head-down orientation.

La natación al revés: estabilidad y maniobrabilidad del pez Aeoliscus punctulatus (Swimming Turned on Its Head: Stability and Maneuverability of the Shrimpfish (Aeoliscus punctulatus)) La orientación típica de un pez neutralmente flotante es con la abertura hacia abajo y la cabeza apuntando hacia delante a lo largo del eje longitudinal. Sin embargo, varios teleósteos avanzados reorientarán el cuerpo verticalmente para comer, ocultarse o agarrarse. El pez Aeoliscus punctulatus mantiene una orientación vertical con la cabeza apuntando hacia abajo. Esta postura se mantiene mediante golpes de las aletas mientras la posición del centro de flotabilidad casi corresponde al centro de masa. El pez nada con el dorso del cuerpo en movimiento anterior. Las secciones transversales del cuerpo tienen un diseño fusiforme con un borde delantero redondeado en el dorso y un borde posterior que se estrecha en la abertura. Las aletas medianas (dorsales, caudales, anales) se colocan a lo largo de la abertura del cuerpo y se golpean o se usan como un timón pasivo para efectuar el movimiento del cuerpo en concierto con los movimientos activos de las aletas pectorales. Se registraron maniobras de natación en ráfaga y de vueltas por guiñada a 500 cuadros/s. La velocidad máxima natación en ráfaga fue de 2, 3 longitudes corporales/s, pero cuando se midió con respecto a la orientación corporal, la velocidad máxima fue de 14, 1 profundidades corporales/s. La velocidad máxima de vuelta por desviarse alrededor del eje longitudinal fue de 957, 5 grados/s. Tal rendimiento de natación está en línea con los peces con una orientación típica. La modificación del diseño del cuerpo y la posición de las aletas permite que el pez Aeoliscus punctulatus nade efectivamente en la orientación de cabeza hacia abajo. Translated to Spanish by YE Jimenez (yordano_jimenez@brown.edu).

A natação de cabeça para baixo: Estabilidade e manobrabilidade do peixe-camarão (Aeoliscus punctulatus) (Swimming Turned on Its Head: Stability and Maneuverability of the Shrimpfish (Aeoliscus punctulatus)) A orientação típica de um peixe de flutuação neutra é com o ventre para baixo e a cabeça apontada anteriormente ao longo do eixo de oscilação longitudinal. No entanto, vários teleósteos derivados reorientam o corpo verticalmente para alimentação, ocultação ou prensão. O peixe-camarão (Aeoliscus punctulatus) mantém uma orientação vertical com a cabeça apontada para baixo. Essa postura é mantida pelo batimento das nadadeiras, já que a posição do centro de empuxo quase corresponde ao centro de massa. O peixe-camarão nada com o dorso do corpo movendo-se anteriormente. As seções transversais do corpo têm um desenho fusiforme com uma borda de ataque arredondada no dorso e uma de fuga no ventre. As nadadeiras medianas (dorsal, caudal e anal) são posicionadas ao longo do ventre e são batidas ou usadas como um leme passivo para efetuar o movimento do corpo em conjunto com os movimentos batidos das nadadeiras peitorais. As manobras explosivas de natação e de guinada foram registradas a 500 quadros por segundo. A velocidade máxima de explosão foi de 2, 3 comprimentos de corpo por segundo, mas quando medida em relação à orientação do corpo, a velocidade máxima foi de 14, 1 vezes a profundidade do corpo por segundo. A taxa máxima de rotação através da guinada em torno do eixo longitudinal foi de 957, 5 graus por segundo. Esse desempenho de natação está de acordo com peixes com uma orientação típica. A modificação do desenho do corpo e a posição das barbatanas permitem que os peixes-camarão nadem efetivamente de cabeça para baixo. Translated to Portuguese by G Sobral (gabisobral@gmail.com).

Body Flexibility Enhances Maneuverability in the World's Largest Predator.

Blue whales are often characterized as highly stable, open-ocean swimmers who sacrifice maneuverability for long-distance cruising performance. However, recent studies have revealed that blue whales actually exhibit surprisingly complex underwater behaviors, yet little is known about the performance and control of these maneuvers. Here, we use multi-sensor biologgers equipped with cameras to quantify the locomotor dynamics and the movement of the control surfaces used by foraging blue whales. Our results revealed that simple maneuvers (rolls, turns, and pitch changes) are performed using distinct combinations of control and power provided by the flippers, the flukes, and bending of the body, while complex trajectories are structured by combining sequences of simple maneuvers. Furthermore, blue whales improve their turning performance by using complex banked turns to take advantage of their substantial dorso-ventral flexibility. These results illustrate the important role body flexibility plays in enhancing control and performance of maneuvers, even in the largest of animals. The use of the body to supplement the performance of the hydrodynamically active surfaces may represent a new mechanism in the control of aquatic locomotion.

Biomechanical model of batoid (skates and rays) pectoral fins predicts the influence of skeletal structure on fin kinematics: implications for bio-inspired design.

Growing interest in the development of bio-inspired autonomous underwater vehicles (AUVs) has motivated research in understanding the mechanisms behind the propulsion systems of marine animals. For example, the locomotive behavior of rays (Batoidea) by movement of the pectoral fins is of particular interest due to their superior performance characteristics over contemporary AUV propulsion systems. To better understand the mechanics of pectoral fin propulsion, this paper introduces a biomechanical model that simulates how batoid skeletal structures function to achieve the swimming locomotion observed in nature. Two rays were studied, Dasyatis sabina (Atlantic ray), and Rhinoptera bonasus (cownose ray). These species were selected because they exhibit very different swimming styles (undulation versus oscillation), but all use primarily their pectoral fins for propulsion (unlike electric rays or guitarfishes). Computerized tomography scans of each species were taken to image the underlying structure, which reveal a complex system of cartilaginous joints and linkages. Data collected from these images were used to quantify the complete skeletal morphometry of each batoid fin. Morphological differences were identified in the internal cartilage arrangement between each species including variations in the orientation of the skeletal elements, or radials, and the joint patterns between them, called the inter-radial joint pattern. These data were used as the primary input into the biomechanical model to couple a given ray skeletal structure with various swimming motions. A key output of the model is an estimation of the uniaxial strain that develops in the skeletal connective tissue in order for the structure to achieve motions observed during swimming. Tensile load tests of this connective tissue were conducted to further investigate the implications of the material strain predictions. The model also demonstrates that changes in the skeletal architecture (e.g., joint positioning) will effect fin deformation characteristics. Ultimately, the results of this study can be used to guide the design of optimally performing bio-inspired AUVs.

Comparison of real and idealized cetacean flippers.

When a phenomenon in nature is mimicked for practical applications, it is often done so in an idealized fashion, such as representing the shape found in nature with convenient, piece-wise smooth mathematical functions. The aim of idealization is to capture the advantageous features of the natural phenomenon without having to exactly replicate it, and it is often assumed that the idealization process does in fact capture the relevant geometry. We explored the consequences of the idealization process by creating exact scale models of cetacean flippers using CT scans, creating corresponding idealized versions and then determining the hydrodynamic characteristics of the models via water tunnel testing. We found that the majority of the idealized models did not exhibit fluid dynamic properties that were drastically different from those of the real models, although multiple consequences resulting from the idealization process were evident. Drag performance was significantly improved by idealization. Overall, idealization is an excellent way to capture the relevant effects of a phenomenon found in nature, which spares the researcher from having to painstakingly create exact models, although we have found that there are situations where idealization may have unintended consequences such as one model that exhibited a decrease in lift performance.

Energetics of terrestrial locomotion of the platypus Ornithorhynchus anatinus.

The platypus Ornithorhynchus anatinus Shaw displays specializations in its limb structure for swimming that could negatively affect its terrestrial locomotion. Platypuses walked on a treadmill at speeds of 0.19-1.08 m x s(-1). Video recordings were used for gait analysis, and the metabolic rate of terrestrial locomotion was studied by measuring oxygen consumption. Platypuses used walking gaits (duty factor >0.50) with a sprawled stance. To limit any potential interference from the extensive webbing on the forefeet, platypuses walk on their knuckles. Metabolic rate increased linearly over a 2.4-fold range with increasing walking speed in a manner similar to that of terrestrial mammals, but was low as a result of the relatively low standard metabolic rate of this monotreme. The dimensionless cost of transport decreased with increasing speed to a minimum of 0.79. Compared with the cost of transport for swimming, the metabolic cost for terrestrial locomotion was 2.1 times greater. This difference suggests that the platypus may pay a price in terrestrial locomotion by being more aquatically adapted than other semi-aquatic or terrestrial mammals.

Biomechanics and energetics in aquatic and semiaquatic mammals: platypus to whale.

A variety of mammalian lineages have secondarily invaded the water. To locomote and thermoregulate in the aqueous medium, mammals developed a range of morphological, physiological, and behavioral adaptations. A distinct difference in the suite of adaptations, which affects energetics, is apparent between semiaquatic and fully aquatic mammals. Semiaquatic mammals swim by paddling, which is inefficient compared to the use of oscillating hydrofoils of aquatic mammals. Semiaquatic mammals swim at the water surface and experience a greater resistive force augmented by wave drag than submerged aquatic mammals. A dense, nonwettable fur insulates semiaquatic mammals, whereas aquatic mammals use a layer of blubber. The fur, while providing insulation and positive buoyancy, incurs a high energy demand for maintenance and limits diving depth. Blubber contours the body to reduce drag, is an energy reserve, and suffers no loss in buoyancy with depth. Despite the high energetic costs of a semiaquatic existence, these animals represent modern analogs of evolutionary intermediates between ancestral terrestrial mammals and their fully aquatic descendants. It is these intermediate animals that indicate which potential selection factors and mechanical constraints may have directed the evolution of more derived aquatic forms.

Energetics of locomotion by the Australian water rat (Hydromys chrysogaster): a comparison of swimming and running in a semi-aquatic mammal.

Semi-aquatic mammals occupy a precarious evolutionary position, having to function in both aquatic and terrestrial environments without specializing in locomotor performance in either environment. To examine possible energetic constraints on semi-aquatic mammals, we compared rates of oxygen consumption for the Australian water rat (Hydromys chrysogaster) using different locomotor behaviors: swimming and running. Aquatic locomotion was investigated as animals swam in a water flume at several speeds, whereas water rats were run on a treadmill to measure metabolic effort during terrestrial locomotion. Water rats swam at the surface using alternate pelvic paddling and locomoted on the treadmill using gaits that included walk, trot and half-bound. Water rats were able to run at twice their maximum swimming velocity. Swimming metabolic rate increased with velocity in a pattern similar to the 'humps' and 'hollows' for wave drag experienced by bodies moving at the water surface. Metabolic rate increased linearly during running. Over equivalent velocities, the metabolic rate for running was 13-40 % greater than for swimming. The minimum cost of transport for swimming (2.61 J N-1 m-1) was equivalent to values for other semi-aquatic mammals. The lowest cost for running (2.08 J N-1 m-1) was 20 % lower than for swimming. When compared with specialists at the extremes of the terrestrial-aquatic continuum, the energetic costs of locomoting either in water or on land were high for the semi-aquatic Hydromys chrysogaster. However, the relative costs for H. chrysogaster were lower than when an aquatic specialist attempts to move on land or a terrestrial specialist attempts to swim.

Comparative kinematics and hydrodynamics of odontocete cetaceans: morphological and ecological correlates with swimming performance.

Propulsive morphology and swimming performance were compared for the odontocete cetaceans Delphinapterus leucas, Orcinus orca, Pseudorca crassidens and Tursiops truncatus. Morphological differences were apparent among the whales. The general body contour and low-aspect-ratio caudal flukes of D. leucas indicated that this species was a low-performance swimmer compared with the other species. Propulsive motions were video-taped as animals swam steadily in large pools. Video tapes were analyzed digitally using a computerized motion-analysis system. Animals swam at relative velocities ranging from 0.4 to 2.4 body lengths s-1. The stroke amplitude of the flukes decreased linearly with velocity for D. leucas, but amplitude remained constant for the other species. Tail-beat frequencies were directly related to relative swimming velocity, whereas the pitch angle of the flukes was inversely related to relative swimming velocity. Unsteady lifting-wing theory was used with regression equations based on kinematics to calculate thrust power output, drag coefficients and propulsive efficiency. Compared with other species, O. orca generated the largest thrust power (36.3 kW) and had the lowest drag coefficient (0.0026), whereas T. truncatus displayed the largest mass-specific thrust power (23.7 W kg-1) and P. crassidens had the highest efficiency (0.9). D. leucas did not swim as rapidly as the other species and had a comparatively higher minimum drag coefficient (0.01), lower mass-specific thrust power (5.2 W kg-1) and lower maximum efficiency (0.84). Minimum drag coefficients were associated with high swimming speeds, and maximum efficiencies corresponded with velocities in the range of typical cruising speeds. The results indicate that the kinematics of the propulsive flukes and hydrodynamics are associated with the swimming behaviors and morphological designs exhibited by the whales in this study, although additional factors will influence morphology.

Energetics of swimming by the platypus Ornithorhynchus anatinus: metabolic effort associated with rowing.

The metabolism of swimming in the platypus Ornithorhynchus anatinus Shaw was studied by measurement of oxygen consumption in a recirculating water flume. Platypuses swam against a constant water current of 0.45-1.0 ms-1. Animals used a rowing stroke and alternated bouts of surface and submerged swimming. Metabolic rate remained constant over the range of swimming speeds tested. The cost of transport decreased with increasing velocity to a minimum of 0.51 at 1.0 ms-1. Metabolic rate and cost of transport for the platypus were lower than values for semiaquatic mammals that swim at the water surface using a paddling mode. However, relative to transport costs for fish, the platypus utilized energy at a similar level to highly derived aquatic mammals that use submerged swimming modes. The efficient aquatic locomotion of the platypus results from its specialised rowing mode in conjunction with enlarged and flexible forefeet for high thrust generation and a behavioral strategy that reduces drag and energy cost by submerged swimming.

Hydrodynamic design of the humpback whale flipper.

The humpback whale (Megaptera novaeangliae) is reported to use its elongate pectoral flippers during swimming maneuvers. The morphology of the flipper from a 9.02-m whale was evaluated with regard to this hydrodynamic function. The flipper had a wing-like, high aspect ratio planform. Rounded tubercles were regularly interspersed along the flipper's leading edge. The flipper was cut into 71 2.5-cm cross-sections and photographed. Except for sections near the distal tip, flipper sections were symmetrical with no camber. Flipper sections had a blunt, rounded leading edge and a highly tapered trailing edge. Placement of the maximum thickness placement for each cross-section varied from 49% of chord at the tip to 19% at mid-span. Section thickness ratio averaged 0.23 with a range of 0.20-0.28. The humpback whale flipper had a cross-sectional design typical of manufactured aerodynamic foils for lift generation. The morphology and placement of leading edge tubercles suggest that they function as enhanced lift devices to control flow over the flipper and maintain lift at high angles of attack. The morphology of the humpback whale flipper suggests that it is adapted for high maneuverability associated with the whale's unique feeding behavior.

Kinematics and estimated thrust production of swimming harp and ringed seals.

The propulsive motions of swimming harp seals (Phoca groenlandica Erxleben) and ringed seals (Phoca hispida Schreber) were studied by filming individuals in a flume. The seals swam at velocities ranging from 0.6 to 1.42 m s-1. Locomotion was accomplished with alternate lateral sweeps of the hind flippers generated by lateral flexions of the axial body in conjunction with flexion of the flippers. The frequency of the propulsive cycle increased linearly with the swimming velocity, and the maximum angle of attack of the flipper decreased, but the amplitude remained constant. The kinematics and morphology of this hind flipper motion indicated that phocid seals do not swim in the carangiform mode as categorized by Lighthill (1969), but in a distinct mode that mimics swimming by thunniform propulsors. The hind flippers acted as hydrofoils, and the efficiency, thrust power and coefficient of thrust were calculated from unsteady wing theory. The propulsive efficiency was high at approximately 0.85. The thrust power increased curvilinearly with velocity. The drag coefficient ranged from 0.012 to 0.028 and was found to be 2.8-7.0 times higher than the theoretical minimum. The drag coefficient was high compared with that of phocid seals examined during gliding or towing experiments, indicating an increased drag encumbered by actively swimming seals. It was determined that phocid seals are capable of generating sufficient power for swimming with turbulent boundary layer conditions.

Mechanics, power output and efficiency of the swimming muskrat (Ondatra zibethicus).

The surface swimming of muskrats (Ondatra zibethicus Linnaeus) was studied by forcing individual animals to swim against a constant water current, of velocity ranging from 0.2 to 0.75 m s-1, in a recirculating water channel. Lateral and ventral views of the swimming muskrats were filmed simultaneously for analysis of thrust by the propulsive appendages. Drag measurements and flow visualization on dead muskrats demonstrated that these animals experience large resistive forces due to the formation of waves and a turbulent wake, because of the pressure and gravitational components which dominate the drag force. Biomechanical analysis demonstrated that thrust is mainly generated by alternating strokes of the hindfeet in the paddling mode. A general lengthening of the hindfeet and presence of lateral fringe hairs on each digit increase the surface area of the foot to produce thrust more effectively during the power phase of the stroke cycle. Increased energy loss from drag on the foot during the recovery phase is minimized by configural and temporal changes of the hindfoot. Employing the models developed by Blake (1979, 1980a,b) for paddle propulsion, it was found that as the arc through which the hindfeet were swept increased with increasing velocity the computed thrust power increased correspondingly. However, the frequency of the stroke cycle remained relatively constant across all velocities at a level of 2.5 Hz. Both mechanical and aerobic efficiencies rose to a maximum with increasing swimming velocity. The aerobic efficiency, which examined the transformation of metabolic power input to thrust power output reached a value of 0.046 at 0.75 m s-1. The mechanical efficiency expressing the relationship of the thrust power generated by the paddling hindfeet and laterally compressed tail (Fish, 1982a,b) to the total mechanical power developed by the propulsive appendages increased to a maximum of 0.33 at 0.75 m s-1. I conclude that the paddling mode of swimming in the muskrat is relatively inefficient when compared to swimming modes which maintain a nearly continuous thrust force over the entire propulsive cycle. However, the paddling mode permits the muskrat to generate propulsive forces effectively while swimming at the surface. The evolution of this mode for semi-aquatic mammals represents only a slight modification from a terrestrial type of locomotion.

Metabolic effects of swimming velocity and water temperature in the muskrat (Ondatra zibethicus).

Metabolic rates, VO2, were studied in four muskrats (Ondatra zibethicus) swimming in a water channel at velocities of 0.2 to 0.75 m/s in water at temperatures of 25 and 30 degrees C. At both water temperatures, VO2 increased linearly with increasing swimming velocity. The VO2 was higher for muskrats swimming in water at 25 than 30 degrees C. The metabolic performance of swimming appears to be influenced by the interaction of swimming velocity and water temperature.