Fish-like three-dimensional swimming with an autonomous, multi-fin, and biomimetic robot.

Fish migrate across considerable distances and exhibit remarkable agility to avoid predators and feed. Fish swimming performance and maneuverability remain unparalleled when compared to robotic systems, partly because previous work has focused on robots and flapping foil systems that are either big and complex, or tethered to external actuators and power sources. By contrast, we present a robot-the Finbot-that combines high degrees of autonomy, maneuverability, and biomimicry with miniature size (160 cm3). Thus, it is well-suited for controlled three-dimensional experiments on fish swimming in confined laboratory test beds. Finbot uses four independently controllable fins and sensory feedback for precise closed-loop underwater locomotion. Different caudal fins can be attached magnetically to reconfigure Finbot for swimming at top speed (122 mm s-1≡ 1 BL s-1) or minimal cost of transport (CoT = 8.2) at Strouhal numbers as low as 0.53. We conducted more than 150 experiments with 12 different caudal fins to measure three key characteristics of swimming fish: (i) linear speed-frequency relationships, (ii) U-shaped CoT, and (iii) reverse Kármán wakes (visualized with particle image velocimetry). More fish-like wakes appeared where the CoT was low. By replicating autonomous multi-fin fish-like swimming, Finbot narrows the gap between fish and fish-like robots and can address open questions in aquatic locomotion, such as optimized propulsion for new fish robots, or the hydrodynamic principles governing the energy savings in fish schools.

Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model.

Fish locomotion is characterized by waves of muscle electrical activity that proceed from head to tail, and result in an undulatory pattern of body bending that generates thrust during locomotion. Isolating the effects of parameters like body stiffness, co-activation between the right and left sides of the body, and frequency on thrust generation has proven to be difficult in live fishes. We use a pneumatically-actuated fish-like model to investigate how these parameters affect locomotor force generation. We measure thrust as well as side forces and torques generated during propulsion. Using a statistical linear model we examine the effects of input parameter combinations on thrust generation. We show that both stiffness and frequency substantially affect swimming kinematics, and that there are complex interactive effects of these two parameters on thrust. The stiffer the backbone the more impact that increasing frequency has on thrust production. For stiffer models, increasing frequency resulted in higher values for both thrust and lateral forces. Large side forces reduce swimming efficiency but this effect could be mitigated by decreasing undulatory wavelength and allowing appropriate phasing of left and right body movements to reduce amplitudes of side force.

Tuna robotics: A high-frequency experimental platform exploring the performance space of swimming fishes.

Tuna and related scombrid fishes are high-performance swimmers that often operate at high frequencies, especially during behaviors such as escaping from predators or catching prey. This contrasts with most fish-like robotic systems that typically operate at low frequencies (< 2 hertz). To explore the high-frequency fish swimming performance space, we designed and tested a new platform based on yellowfin tuna (Thunnus albacares) and Atlantic mackerel (Scomber scombrus). Body kinematics, speed, and power were measured at increasing tail beat frequencies to quantify swimming performance and to study flow fields generated by the tail. Experimental analyses of freely swimming tuna and mackerel allow comparison with the tuna-like robotic system. The Tunabot (255 millimeters long) can achieve a maximum tail beat frequency of 15 hertz, which corresponds to a swimming speed of 4.0 body lengths per second. Comparison of midline kinematics between scombrid fish and the Tunabot shows good agreement over a wide range of frequencies, with the biggest discrepancy occurring at the caudal fin, primarily due to the rigid propulsor used in the robotic model. As frequency increases, cost of transport (COT) follows a fish-like U-shaped response with a minimum at ~1.6 body lengths per second. The Tunabot has a range of ~9.1 kilometers if it swims at 0.4 meter per second or ~4.2 kilometers at 1.0 meter per second, assuming a 10-watt-hour battery pack. These results highlight the capabilities of high-frequency biological swimming and lay the foundation to explore a fish-like performance space for bio-inspired underwater vehicles.

Fish optimize sensing and respiration during undulatory swimming.

Previous work in fishes considers undulation as a means of propulsion without addressing how it may affect other functions such as sensing and respiration. Here we show that undulation can optimize propulsion, flow sensing and respiration concurrently without any apparent tradeoffs when head movements are coupled correctly with the movements of the body. This finding challenges a long-held assumption that head movements are simply an unintended consequence of undulation, existing only because of the recoil of an oscillating tail. We use a combination of theoretical, biological and physical experiments to reveal the hydrodynamic mechanisms underlying this concerted optimization. Based on our results we develop a parsimonious control architecture that can be used by both undulatory animals and machines in dynamic environments.

Caudal fin shape modulation and control during acceleration, braking and backing maneuvers in bluegill sunfish, Lepomis macrochirus.

Evolutionary patterns of intrinsic caudal musculature in ray-finned fishes show that fine control of the dorsal lobe of the tail evolved first, followed by the ability to control the ventral lobe. This progression of increasing differentiation of musculature suggests specialization of caudal muscle roles. Fine control of fin elements is probably responsible for the range of fin conformations observed during different maneuvering behaviors. Here, we examine the kinematics of the caudal fin and the motor activity of the intrinsic caudal musculature during kick-and-glide, braking and backing maneuvers, and compare these data with our previous work on the function of the caudal fin during steady swimming. Kick-and-glide maneuvers consisted of large-amplitude, rapid lateral excursion of the tail fin, followed by forward movement of the fish with the caudal fin rays adducted to reduce surface area and with the tail held in line with the body. Just before the kick, the flexors dorsalis and ventralis, hypochordal longitudinalis, infracarinalis and supracarinalis showed strong activity. During braking, the dorsal and ventral lobes of the tail moved in opposite directions, forming an ;S'-shape, accompanied by strong activity in the interradialis muscles. During backing up, the ventral lobe initiated a dorsally directed wave along the distal edge of the caudal fin. The relative timing of the intrinsic caudal muscles varied between maneuvers, and their activation was independent of the activity of the red muscle of the axial myomeres in the caudal region. There was no coupling of muscle activity duration and electromyographic burst intensity in the intrinsic caudal muscles during maneuvers, as was observed in previous work on steady swimming. Principal-component analysis produced four components that cumulatively explained 73.6% of the variance and segregated kick-and-glide, braking and backing maneuvers from each other and from steady swimming. The activity patterns of the intrinsic caudal muscles during maneuvering suggest motor control independent from myotomal musculature, and specialization of individual muscles for specific kinematic roles.

Hydrodynamic function of dorsal and anal fins in brook trout (Salvelinus fontinalis).

Recent kinematic and hydrodynamic studies on fish median fins have shown that dorsal fins actively produce jets with large lateral forces. Because of the location of dorsal fins above the fish's rolling axis, these lateral forces, if unchecked, would cause fish to roll. In this paper we examine the hydrodynamics of trout anal fin function and hypothesize that anal fins, located below the fish's rolling axis, produce similar jets to the dorsal fin and help balance rolling torques during swimming. We simultaneously quantify the wake generated by dorsal and anal fins in brook trout by swimming fish in two horizontal light sheets filmed by two synchronized high speed cameras during steady swimming and manoeuvring. Six major conclusions emerge from these experiments. First, anal fins produce lateral jets to the same side as dorsal fins, confirming the hypothesis that anal fins produce fluid jets that balance those produced by dorsal fins. Second, in contrast to previous work on sunfish, neither dorsal nor anal fins produce significant thrust during steady swimming; flow leaves the dorsal and anal fins in the form of a shear layer that rolls up into vortices similar to those seen in steady swimming of eels. Third, dorsal and anal fin lateral jets are more coincident in time than would be predicted from simple kinematic expectations; shape, heave and pitch differences between fins, and incident flow conditions may account for the differences in timing of jet shedding. Fourth, relative force and torque magnitudes of the anal fin are larger than those of the dorsal fin; force differences may be due primarily to a larger span and a more squarely shaped trailing edge of the anal fin compared to the dorsal fin; torque differences are also strongly influenced by the location of each fin relative to the fish's centre of mass. Fifth, flow is actively modified by dorsal and anal fins resulting in complex flow patterns surrounding the caudal fin. The caudal fin does not encounter free-stream flow, but rather moves through incident flow greatly altered by the action of dorsal and anal fins. Sixth, trout anal fin function differs from dorsal fin function; although dorsal and anal fins appear to cooperate functionally, there are complex interactions between other fins and free stream perturbations that require independent dorsal and anal fin motion and torque production to maintain control of body position.

Dorsal and anal fin function in bluegill sunfish Lepomis macrochirus: three-dimensional kinematics during propulsion and maneuvering.

Dorsal and anal fins are median fins located above and below the centre of mass of fishes, each having a moment arm relative to the longitudinal axis. Understanding the kinematics of dorsal and anal fins may elucidate how these fins are used in concert to maintain and change fish body position and yet little is known about the functions of these fins. Using three synchronized high-speed cameras (500 frames s(-1)) we studied the three-dimensional kinematics of dorsal and anal fins during steady swimming (0.5-2.5 TL s(-1), where TL = total length) and during slow speed maneuvers (0.5 TL s(-1)). By digitizing points along every other fin ray in the soft-rayed portion of the fins we were able to determine not only the movement of the fin surface but also the curvature of individual fin rays and the resulting fin surface shape. We found that dorsal and anal fins begin oscillating, in phase, at steady swimming speeds above 1.0 TL s(-1) and that maximum lateral displacement of the trailing edge of the fins as well as fin area increase with increasing steady swimming speed. Differences in area, lateral displacement and moment arm between the dorsal and anal fin suggest that dorsal and anal fins produce balancing torques during steady swimming. During maneuvers, fin area is maximized and mean lateral excursion of both fins is greater than during steady swimming, with large variation among maneuvers. Fin surface shape changes dramatically during maneuvers. At any given point in time the spanwise (base to tip) curvature along fin rays can differ between adjacent rays, suggesting that fish have a high level of control over fin surface shape. Also, during maneuvers the whole surface of both dorsal and anal fins can be bent without individual fin rays exhibiting significant curvature.

Biomechanics: hydrodynamic function of the shark's tail.

The tail of most sharks has an elongated upper lobe that differs from the externally symmetrical tail structure common among bony fishes, but the hydrodynamic purpose of this asymmetric tail shape is unclear. Here we quantify water flow patterns in the wakes of freely swimming dogfish sharks and find that they have a ring-within-a-ring vortex structure, in contrast to the single rings shed by symmetrical fish tails. The branched-ring vortex is generated by the inclined angle of the tail's trailing edge and by its motion at an angle to the horizontal body axis; the vortex directs water backwards and downwards, which may increase the shark's vertical manoeuvrability.

Function of the heterocercal tail in sharks: quantitative wake dynamics during steady horizontal swimming and vertical maneuvering.

The function of the heterocercal tail in sharks has long been debated in the literature. Previous kinematic data have supported the classical theory which proposes that the beating of the heterocercal caudal fin during steady horizontal locomotion pushes posteroventrally on the water, generating a reactive force directed anterodorsally and causing rotation around the center of mass. An alternative model suggests that the heterocercal shark tail functions to direct reaction forces through the center of mass. In this paper, we quantify the function of the tail in two species of shark and compare shark tail function with previous hydrodynamic data on the heterocercal tail of sturgeon Acipenser transmontanus. To address the two models of shark heterocercal tail function, we applied the technique of digital particle image velocimetry (DPIV) to quantify the wake of two species of shark swimming in a flow tank. Both steady horizontal locomotion and vertical maneuvering were analyzed. We used DPIV with both horizontal and vertical light sheet orientations to quantify patterns of wake velocity and vorticity behind the heterocercal tail of leopard sharks (Triakis semifasciata) and bamboo sharks (Chiloscyllium punctatum) swimming at 1.0Ls(-1), where L is total body length. Two synchronized high-speed video cameras allowed simultaneous measurement of shark body position and wake structure. We measured the orientation of tail vortices shed into the wake and the orientation of the central jet through the core of these vortices relative to body orientation. Analysis of flow geometry indicates that the tail of both leopard and bamboo shark generates strongly tilted vortex rings with a mean jet angle of approximately 30 degrees below horizontal during steady horizontal swimming. The corresponding angle of the reaction force is much greater than body angle (mean 11 degrees ) and the angle of the path of motion of the center of mass (mean approximately 0 degrees ), thus strongly supporting the classical model of heterocercal tail function for steady horizontal locomotion. Vortex jet angle varies significantly with body angle changes during vertical maneuvering, but sharks show no evidence of active reorientation of jet angle relative to body angle, as was seen in a previous study on the function of sturgeon tail. Vortex jet orientation is significantly more inclined than the relatively horizontal jet generated by sturgeon tail vortex rings, demonstrating substantial differences in function in the heterocercal tails of sharks and sturgeon. We present a summary of forces on a swimming shark integrating data obtained here on the tail with previous data on pectoral fin and body function. Body orientation plays a critical role in the overall force balance and compensates for torques generated by the tail. The pectoral fins do not generate lift during steady horizontal locomotion, but play an important hydrodynamic role during vertical maneuvering.

Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish.

A key evolutionary transformation of the locomotor system of ray-finned fishes is the morphological elaboration of the dorsal fin. Within Teleostei, the dorsal fin primitively is a single midline structure supported by soft, flexible fin rays. In its derived condition, the fin is made up of two anatomically distinct portions: an anterior section supported by spines, and a posterior section that is soft-rayed. We have a very limited understanding of the functional significance of this evolutionary variation in dorsal fin design. To initiate empirical hydrodynamic study of dorsal fin function in teleost fishes, we analyzed the wake created by the soft dorsal fin of bluegill sunfish (Lepomis macrochirus) during both steady swimming and unsteady turning maneuvers. Digital particle image velocimetry was used to visualize wake structures and to calculate in vivo locomotor forces. Study of the vortices generated simultaneously by the soft dorsal and caudal fins during locomotion allowed experimental characterization of median-fin wake interactions. During high-speed swimming (i.e. above the gait transition from pectoral- to median-fin locomotion), the soft dorsal fin undergoes regular oscillatory motion which, in comparison with analogous movement by the tail, is phase-advanced (by 30% of the cycle period) and of lower sweep amplitude (by 1.0 cm). Undulations of the soft dorsal fin during steady swimming at 1.1 bodylength s(-1) generate a reverse von Kármán vortex street wake that contributes 12% of total thrust. During low-speed turns, the soft dorsal fin produces discrete pairs of counterrotating vortices with a central region of high-velocity jet flow. This vortex wake, generated in the latter stage of the turn and posterior to the center of mass of the body, counteracts torque generated earlier in the turn by the anteriorly positioned pectoral fins and thereby corrects the heading of the fish as it begins to translate forward away from the turning stimulus. One-third of the laterally directed fluid force measured during turning is developed by the soft dorsal fin. For steady swimming, we present empirical evidence that vortex structures generated by the soft dorsal fin upstream can constructively interact with those produced by the caudal fin downstream. Reinforcement of circulation around the tail through interception of the dorsal fin's vortices is proposed as a mechanism for augmenting wake energy and enhancing thrust. Swimming in fishes involves the partitioning of locomotor force among several independent fin systems. Coordinated use of the pectoral fins, caudal fin and soft dorsal fin to increase wake momentum, as documented for L. macrochirus, highlights the ability of teleost fishes to employ multiple propulsors simultaneously for controlling complex swimming behaviors.

Locomotion in scombrid fishes: visualization of flow around the caudal peduncle and finlets of the chub mackerel Scomber japonicus.

Scombrid fishes are known for high-performance locomotion; however, few data are available on scombrid locomotor hydrodynamics. In this paper, we present flow visualization data on patterns of water movement over the caudal peduncle and finlets (small fins on the dorsal and ventral body margin anterior to the caudal fin). Chub mackerel, Scomber japonicus, ranging in fork length from 20 to 26 cm, swam steadily at 1.2forklengthss(-1) in a recirculating flow tank. Small, reflective particles in the flow tank were illuminated by a vertical (xy) or horizontal (xz) laser light sheet. Patterns of flow in the region near the caudal peduncle were measured using digital particle image velocimetry. Patterns of flow along the peduncle and finlets were quantified using manual particle tracking; more than 800 particles were tracked for at least 12ms over a series of tailbeats from each of four fish. In the vertical plane, flow trajectory and flow speed were independent of the position of the finlets, indicating that the finlets did not redirect flow or affect flow speed. Along, above and below the trailing surface of the peduncle, where the finlets were oriented along the peduncular surface, flow was convergent. Along, above and below the leading surface of the peduncle, where the finlets were absent, the flow trajectory was effectively horizontal. The lack of divergent flow on the leading surface of the peduncle is consistent with cross-peduncular flow formed by the lateral motion of the peduncle interacting with convergent flow resulting from forward movement of the body. In the horizontal plane, particles illuminated by the xz light sheet situated approximately 3 mm below the ventral body surface were tracked within the laser light sheet for up to 40ms, indicating strong planar flow. As the peduncle decelerates, the most posterior finlet is frequently at an angle of attack of at least 20 degrees to the incident flow, but this orientation does not result in thrust production from lift generation. Finlet 5 does redirect cross-peduncular flow and probably generates small vortices undetectable in this study. These data are the first direct demonstration that the finlets have a hydrodynamic effect on local flow during steady swimming.

Functional morphology of the pectoral fins in bamboo sharks, Chiloscyllium plagiosum: benthic vs. pelagic station-holding.

Bamboo sharks (Chiloscyllium plagiosum) are primarily benthic and use their relatively flexible pectoral and pelvic fins to rest on and move about the substrate. We examined the morphology of the pectoral fins and investigated their locomotory function to determine if pectoral fin function during both benthic station-holding and pelagic swimming differs from fin function described previously in leopard sharks, Triakis semifasciata. We used three-dimensional kinematics and digital particle image velocimetry (DPIV) to quantify pectoral fin function in five white-spotted bamboo sharks, C. plagiosum, during four behaviors: holding station on the substrate, steady horizontal swimming, and rising and sinking during swimming. During benthic station-holding in current flow, bamboo sharks decrease body angle and adjust pectoral fin angle to shed a clockwise fluid vortex. This vortex generates negative lift more than eight times that produced during open water vertical maneuvering and also results in an upstream flow that pushes against the posterior surface of the pectoral fin to oppose drag. In contrast, there is no evidence of significant lift force in the wake of the pectoral fin during steady horizontal swimming. The pectoral fin is held concave downward and at a negative dihedral angle during steady horizontal swimming, promoting maneuverability rather than stability, although this negative dihedral angle is much less than that observed previously in sturgeon and leopard sharks. During sinking, the pectoral fins are held concave upward and shed a clockwise vortex with a negative lift force, while in rising the pectoral fin is held concave downward and sheds a counterclockwise vortex with a positive lift force. Bamboo sharks appear to sacrifice maneuverability for stability when locomoting in the water column and use their relatively flexible fins to generate strong negative lift forces when holding position on the substrate and to enhance stability when swimming in the water column.

Aquatic prey capture in ray-finned fishes: a century of progress and new directions.

The head of ray-finned fishes is structurally complex and is composed of numerous bony, muscular, and ligamentous elements capable of intricate movement. Nearly two centuries of research have been devoted to understanding the function of this cranial musculoskeletal system during prey capture in the dense and viscous aquatic medium. Most fishes generate some amount of inertial suction to capture prey in water. In this overview we trace the history of functional morphological analyses of suction feeding in ray-finned fishes, with a particular focus on the mechanisms by which suction is generated, and present new data using a novel flow imaging technique that enables quantification of the water flow field into the mouth. We begin with a brief overview of studies of cranial anatomy and then summarize progress on understanding function as new information was brought to light by the application of various forms of technology, including high-speed cinematography and video, pressure, impedance, and bone strain measurement. We also provide data from a new technique, digital particle image velocimetry (DPIV) that allows us to quantify patterns of flow into the mouth. We believe that there are three general areas in which future progress needs to occur. First, quantitative three-dimensional studies of buccal and opercular cavity dimensions during prey capture are needed; sonomicrometry and endoscopy are techniques likely to yield these data. Second, a thorough quantitative analysis of the flow field into the mouth during prey capture is necessary to understand the effect of head movement on water in the vicinity of the prey; three-dimensional DPIV analyses will help to provide these data. Third, a more precise understanding of the fitness effects of structural and functional variables in the head coupled with rigorous statistical analyses will allow us to better understand the evolutionary consequences of intra- and interspecific variation in cranial morphology and function.

Three-dimensional analysis of finlet kinematics in the chub mackerel (Scomber japonicus).

Finlets, which are small non-retractable fins located on the body margins between the second dorsal and anal fins and the caudal fin of scombrid fishes, have been hypothesized to improve swimming performance. The kinematics of three posterior finlets of the chub mackerel, Scomber japonicus, were examined using three-dimensional measurement techniques to test hypotheses on finlet rigidity and function during steady swimming. Finlet bending and finlet planar orientation to the xz, yz, and xy planes were measured during steady swimming at 1.2 lengths s(-1) in a flow tank. Despite very similar morphology among the individual finlets, there was considerable variability in finlet flexure during a stroke. Several of the finlets were relatively rigid and flat (with intrafinlet angles close to 180 degrees during the stroke), although intrafinlet angle of the proximal portion of the most posterior finlet varied considerably over the stroke and was as low as 140 degrees midstroke. Finlets showed complex orientations in three-dimensional space over a stroke, and these orientations differed among the finlets. For example, during tail deceleration the proximal portion of the fifth finlet achieves a mean angle of approximately 75 degrees with the xz plane, while the distal portion of this finlet is oriented at 110 degrees. Our data suggest that the trajectory of local water flow varies among finlets and that the most posterior finlet is oriented to redirect flow into the developing tail vortex, which may increase thrust produced by the tail of swimming mackerel.

Wake dynamics and fluid forces of turning maneuvers in sunfish.

While experimental analyses of steady rectilinear locomotion in fishes are common, unsteady movement involving time-dependent variation in heading, speed and acceleration probably accounts for the greatest portion of the locomotor time budget. Turning maneuvers, in particular, are key elements of the unsteady locomotor repertoire of fishes and, by many species, are accomplished by generating asymmetrical forces with the pectoral fins. The development of such left-right asymmetries in force production is a critical and as yet unstudied aspect of aquatic locomotor dynamics. In this paper, we measure the fluid forces exerted by the left and right pectoral fins of bluegill sunfish (Lepomis macrochirus) during turning using digital particle image velocimetry (DPIV). DPIV allowed quantification of water velocity fields, and hence momentum, in the wake of the pectoral fins as sunfish executed turns; forces exerted during turning were compared with those generated by the immediately preceding fin beats during steady swimming. Sunfish generate the forces required for turning by modulating two variables: wake momentum and pectoral fin stroke timing. Fins on opposite sides of the fish play functionally distinct roles during turning maneuvers. The fin nearer the stimulus inducing the turn (i.e. the strong side fin) generates a laterally oriented vortex ring with a strong central jet whose associated lateral force is four times greater than that produced during steady swimming. Little posterior (thrust) force is generated by the strong-side fin, and this fin therefore acts to rotate the body away from the source of the stimulus. The contralateral (weak-side) fin generates a posteriorly oriented vortex ring with a thrust force nine times that produced by the fin during steady swimming. Minimal lateral force is exerted by the weak-side fin, and this fin therefore acts primarily to translate the body linearly away from the stimulus. Turning with the paired fins is not simply steady swimming performed unilaterally. Instead, turning involves asymmetrical fin movements and fluid forces that are distinct in both direction and magnitude from those used to swim forward at constant speed. These data reflect the plasticity of the teleost pectoral fin in performing a wide range of steady and unsteady locomotor tasks.

Function of the heterocercal tail in white sturgeon: flow visualization during steady swimming and vertical maneuvering.

Basal ray-finned fishes possess a heterocercal tail in which the dorsal lobe containing the extension of the vertebral column is longer than the ventral lobe. Clarifying the function of the heterocercal tail has proved elusive because of the difficulty of measuring the direction of force produced relative to body position in the aquatic medium. We measured the direction of force produced by the heterocercal tail of the white sturgeon (Acipenser transmontanus) by visualizing flow in the wake of the tail using digital particle image velocimetry (DPIV) while simultaneously recording body position and motion using high-speed video. To quantify tail function, we measured the vertical body velocity, the body angle and the path angle of the body from video recordings and the vortex ring axis angle and vortex jet angle from DPIV recordings of the wake downstream from the tail. These variables were measured for sturgeon exhibiting three swimming behaviors at 1.2 L s(-)(1), where L is total body length: rising through the water column, holding vertical position, and sinking through the water column. For vertical body velocity, body angle and path angle values, all behaviors were significantly different from one another. For vortex ring axis angle and vortex jet angle, rising and holding behavior were not significantly different from each other, but both were significantly different from sinking behavior. During steady horizontal swimming, the sturgeon tail generates a lift force relative to the path of motion but no rotational moment because the reaction force passes through the center of mass. For a rising sturgeon, the tail does not produce a lift force but causes the tail to rotate ventrally in relation to the head since the reaction force passes ventral to the center of mass. While sinking, the direction of the fluid jet produced by the tail relative to the path of motion causes a lift force to be created and causes the tail to rotate dorsally in relation to the head since the reaction force passes dorsal to the center of mass. These data provide evidence that sturgeon can actively control the direction of force produced by their tail while maneuvering through the water column because the relationship between vortex jet angle and body angle is not constant.

A hydrodynamic analysis of fish swimming speed: wake structure and locomotor force in slow and fast labriform swimmers.

Past study of interspecific variation in the swimming speed of fishes has focused on internal physiological mechanisms that may limit the ability of locomotor muscle to generate power. In this paper, we approach the question of why some fishes are able to swim faster than others from a hydrodynamic perspective, using the technique of digital particle image velocimetry which allows measurement of fluid velocity and estimation of wake momentum and mechanical forces for locomotion. We investigate the structure and strength of the wake in three dimensions to determine how hydrodynamic force varies in two species that differ markedly in maximum swimming speed. Black surfperch (Embiotoca jacksoni) and bluegill sunfish (Lepomis macrochirus) swim at low speeds using their pectoral fins exclusively, and at higher speeds switch to combined pectoral and caudal fin locomotion. E. jacksoni can swim twice as fast as similarly sized L. macrochirus using the pectoral fins alone. The pectoral fin wake of black surfperch at all speeds consists of two distinct vortex rings linked ventrally. As speed increases from 1.0 to 3.0 L s(-)(1), where L is total body length, the vortex ring formed on the fin downstroke reorients to direct force increasingly downstream, parallel to the direction of locomotion. The ratio of laterally to downstream-directed force declines from 0.93 to 0.07 as speed increases. In contrast, the sunfish pectoral fin generates a single vortex ring per fin beat at low swimming speeds and a pair of linked vortex rings (with one ring only partially complete and attached to the body) at maximal labriform speeds. Across a biologically relevant range of swimming speeds, bluegill sunfish generate relatively large lateral forces with the paired fins: the ratio of lateral to downstream force remains at or above 1.0 at all speeds. By increasing wake momentum and by orienting this momentum in a direction more favorable for thrust than for lateral force, black surfperch are able to swim at twice the speed of bluegill sunfish using the pectoral fins. In sunfish, without a reorientation of shed vortices, increases in power output of pectoral fin muscle would have little effect on maximum locomotor speed. We present two hypotheses relating locomotor stability, maneuverability and the structure of the vortex wake. First, at low speeds, the large lateral forces exhibited by both species may be necessary for stability. Second, we propose a potential hydrodynamic trade-off between speed and maneuverability that arises as a geometric consequence of the orientation of vortex rings shed by the pectoral fins. Bluegill sunfish may be more maneuverable because of their ability to generate large mediolateral force asymmetries between the left- and right-side fins.

Locomotion in scombrid fishes: morphology and kinematics of the finlets of the chub mackerel Scomber japonicus.

Finlets are small non-retractable fins located on the dorsal and ventral margins of the body between the second dorsal and anal fins and the tail of scombrid fishes. The morphology of the finlets, and finlet kinematics during swimming in a flow tank at speeds of 0.8-3. 0 fork lengths s(-1), were examined in the chub mackerel Scomber japonicus. Functionally, S. japonicus has five dorsal and anal triangular finlets (the fifth finlet is a pair of finlets acting in concert). Slips of muscle that insert onto the base of each finlet indicate the potential for active movement. In animals of similar mass, finlet length and area increased posteriorly. Finlet length, height and area show positive allometry in animals from 45 to 279 g body mass. Summed finlet area was approximately 15 % of caudal fin area. During steady swimming, the finlets typically oscillated symmetrically in the horizontal and vertical planes. Finlet excursions in the x, y and z directions ranged from 1 to 5 mm, increased posteriorly and were independent of speed. The timing of the maximum amplitude of oscillation was phased posteriorly; the phase lag of the maximum amplitude of oscillation was independent of speed. During some periods of gliding, a finlet occasionally moved independently of the body and the other finlets, which indicated active control of finlet movement. The angle of attack of the finlets averaged approximately 0 degrees over a tailbeat, indicating no net contribution to thrust production via classical lift-based mechanisms. However, the timing of finlet movement relative to that of the tail suggests that more posterior finlets may direct some flow longitudinally as the tail decelerates and thereby contribute flow to the developing caudal fin vortex.

Three-dimensional kinematics and wake structure of the pectoral fins during locomotion in leopard sharks Triakis semifasciata.

The classical theory of locomotion in sharks proposes that shark pectoral fins are oriented to generate lift forces that balance the moment produced by the oscillating heterocercal tail. Accordingly, previous studies of shark locomotion have used fixed-wing aircraft as a model assuming that sharks have similar stability and control mechanisms. However, unlike airplanes, sharks are propelled by undulations of the body and tail and have considerable control of pectoral fin motion. In this paper, we use a new approach to examine the function of the pectoral fins of leopard sharks, Triakis semifasciata, during steady horizontal swimming at speeds of 0.5-2.0ls(-1), where l is total body length, and during vertical maneuvering (rising and sinking) in the water column. The planar orientation of the pectoral fin was measured using three-dimensional kinematics, while fluid flow in the wake of the pectoral fin and forces exerted on the water by the fin were quantified using digital particle image velocimetry (DPIV). Steady horizontal swimming in leopard sharks is characterized by continuous undulations of the body with a positive body tilt to the flow that decreases from a mean of 11 degrees to 0.6 degrees with increasing flow speeds from 0. 5 to 2.0ls(-1). Three-dimensional analysis showed that, during steady horizontal locomotion, the pectoral fins are cambered, concave downwards, at a negative angle of attack that we predict to generate no significant lift. Leopard shark pectoral fins are also oriented at a substantial negative dihedral angle that amplifies roll moments and hence promotes rapid changes in body position. Vortices shed from the trailing edge of the pectoral fin were detected only during vertical maneuvering. Starting vortices are produced when the posterior plane of the pectoral fin is actively flipped upwards or downwards to initiate rising or sinking, respectively, in the water column. The starting vortex produced by the pectoral fin induces a pitching moment that reorients the body relative to the flow. Body and pectoral fin surface angle are altered significantly when leopard sharks change vertical position in the water column. Thus, locomotion in leopard sharks is not analogous to flight in fixed-wing aircraft. Instead, a new force balance for swimming leopard sharks is proposed for steady swimming and maneuvering. Total force balance on the body is adjusted by altering the body angle during steady swimming as well as during vertical maneuvering, while the pectoral fins appear to be critical for initiating maneuvering behaviors, but not for lift production during steady horizontal locomotion.