Airfoil-like mechanics generate thrust on the anterior body of swimming fishes

Bioinspired design of a tissue-engineered ray with machine learning

In biomimetic design, researchers recreate existing biological structures to form functional devices. For biohybrid robotic swimmers assembled with tissue engineering, this is problematic because most devices operate at different length scales than their naturally occurring counterparts, resulting in reduced performance. To overcome these challenges, here, we demonstrate how machine learning-directed optimization (ML-DO) can be used to inform the design of a biohybrid robot, outperforming other nonlinear optimization techniques, such as Bayesian optimization, in the selection of high-performance geometries. We show how this approach can be used to maximize the thrust generated by a tissue-engineered mobuliform miniray. This results in devices that can swim at the millimeter scale while more closely preserving natural locomotive scaling laws. Overall, this work provides a quantitatively rigorous approach for the engineering design of muscular structure-function relationships in an automated fashion.

Exploring the swimming performance and the physical mechanisms ofTomopterislocomotion

Tomopterids are mesmerizing holopelagic swimmers. They use two modes of locomotion simultaneously: drag-based metachronal paddling and bodily undulation.Tomopterishas two rows of flexible, leg-like parapodia positioned on opposite sides of its body. Each row metachronally paddles out of phase to the other. Both paddling behaviors occur in concert with a lateral bodily undulation. However, when looked at independently, each mode appears in tension with the other. The direction of the undulatory wave is opposite of what one may expect for forward (FWD) swimming and appears to actively work act against the direction of swimming initiated by metachronal paddling. To investigate how these two modes of locomotion synergize to generate effective swimming, we created a self-propelled, fluid-structure interaction model of an idealizedTomopteris. We holistically explored swimming performance over a 3D mechanospace comprising parapodia length, paddling amplitude, and undulatory amplitude using a machine learning framework based on polynomial chaos expansions. Although undulatory amplitude minimally affected FWD swimming speeds, it helped mitigate the larger costs of transport that arise from either using more mechanically expensive (larger) paddling amplitudes and/or having longer parapodia.

Swimming kinematics of rainbow trout behind a 3×5 cylinder array: a computationally driven experimental approach to understanding fish locomotion

Fish in the wild often contend with complex flows that are produced by natural and artificial structures. Research into fish interactions with turbulence often investigates metrics such as turbulent kinetic energy (TKE) or fish positional location, with less focus on the specific interactions between vortex organization and body swimming kinematics. Here, we compared the swimming kinematics of rainbow trout (Oncorhynchus mykiss) holding station in flows produced by two different 3×5 cylinder arrays. We systematically utilized computational fluid dynamics to identify one array that produced a Kármán vortex street with high vortex periodicity (KVS array) and another that produced low periodicity, similar to a parallel vortex street (PVS array), both validated with particle image velocimetry. The only difference in swimming kinematics between cylinder arrays was an increased tail beat amplitude in the KVS array. In both cylinder arrays, the tail beat frequency decreased and snout amplitude increased compared with the freestream. The center of mass amplitude was greater in the PVS array than in only the freestream, however, suggesting some buffeting of the body by the fluid. Notably, we did not observe Kármán gaiting in the KVS array as in previous studies. We hypothesize that this is because (1) vorticity was dissipated in the region where fish held station or (2) vortices were in-line rather than staggered. These results are the first to quantify the kinematics and behavior of fishes swimming in the wake of multiple cylinder arrays, which has important implications for biomechanics, fluid dynamics and fisheries management.

Swimming kinematics of rainbow trout behind cylinder arrays: the effect of vortex street periodicity and turbulence kinetic energy

Fish in the wild often contend with complex flows that are produced by natural and artificial structures. Research into fish interactions with turbulence often investigates metrics such as turbulence kinetic energy (TKE) or fish positional location, with less attention paid to the specific interactions between vortex organization and body swimming kinematics. Here we compare the swimming kinematics of rainbow trout ( Oncorhynchus mykiss ) holding station in flows produced by two different 3 x 5 cylinder arrays. We systematically utilized computational fluid dynamics to generate one array that produced a Kármán vortex street with high vortex periodicity and TKE (KVS array), and another that produced low periodicity and TKE, similar to a parallel vortex street (PVS array). The only difference in swimming kinematics between cylinder arrays was an increased tail beat amplitude in the KVS array. In both cylinder arrays, the tail beat frequency decreased and snout amplitude increased compared with the freestream. The center of mass amplitude was greater in the PVS array than in only the freestream, however, suggesting some buffeting of the body by the fluid. Notably, we did not observe Kármán gaiting in the KVS array as in previous studies. We hypothesize that this is because (1) vorticity was dissipated in the region where fish held station in this study and (2) cylinder arrays produced vortices that were in-line rather than staggered. These results are the first to quantify the kinematics and behavior of fishes swimming in the wake of multiple cylinder arrays, which has important implications for biomechanics, fluid dynamics, and fisheries management.

SUMMARY STATEMENT

The swimming kinematics of rainbow trout are largely preserved across two, 3 x 5 cylinder array treatments that differed in vortex periodicity and turbulence kinetic energy.

A two-dimensional hydrodynamics prediction framework for mantle-undulated propulsion robot using multiple proper orthogonal decomposition and long short term memory neural network

In this paper, a deep learning based framework has been developed to predict hydrodynamic forces on a mantle-undulated propulsion robot (MUPRo). A multiple proper orthogonal decomposition (MPOD) algorithm has been proposed to efficiently identify fluid features near the undulating mantle of the MUPRo globally and locally. The results indicate that theL2error of the solution states near the undulating boundary of the proposed MPOD algorithm converges almost linearly to 0.2%. Furthermore, a hydrodynamics prediction framework has been developed based on the proposed MPOD algorithm, where a long short-term memory neural network predicts the temporal coefficients of the MPOD spatial modes. The developed framework achieves economical and reliable predictions of hydrodynamic forces acting on the undulating boundary compared to simulations and experiments. Moreover, theL2error of the developed framework is one to two orders of magnitude lower than that of the frameworks based on the classical POD algorithm when the degrees of freedom are consistent. Finally, the reliability of the proposed MPOD-NIROM is discussed through an offline parameter planning case of an aquatic-inspired robot. The model presented in this paper can provide support for the offline parameter planning of aquatic-inspired robots.

Adhesion Behavior in Fish: From Structures to Applications

In nature, some fish can adhere tightly to the surface of stones, aquatic plants, and even other fish bodies. This adhesion behavior allows these fish to fix, eat, hide, and migrate in complex and variable aquatic environments. The adhesion function is realized by the special mouth and sucker tissue of fish. Inspired by adhesion fish, extensive research has recently been carried out. Therefore, this paper presents a brief overview to better explore underwater adhesion mechanisms and provide bionic applications. Firstly, the adhesion organs and structures of biological prototypes (e.g., clingfish, remora, Garra, suckermouth catfish, hill stream loach, and goby) are presented separately, and the underwater adhesion mechanisms are analyzed. Then, based on bionics, it is explained that the adhesion structures and components are designed and created for applications (e.g., flexible gripping adhesive discs and adhesive motion devices). Furthermore, we offer our perspectives on the limitations and future directions.

In-line swimming dynamics revealed by fish interacting with a robotic mechanism

Schooling in fish is linked to a number of factors such as increased foraging success, predator avoidance, and social interactions. In addition, a prevailing hypothesis is that swimming in groups provides energetic benefits through hydrodynamic interactions. Thrust wakes are frequently occurring flow structures in fish schools as they are shed behind swimming fish. Despite increased flow speeds in these wakes, recent modeling work has suggested that swimming directly in-line behind an individual may lead to increased efficiency. However, only limited data are available on live fish interacting with thrust wakes. Here we designed a controlled experiment in which brook trout, Salvelinus fontinalis, interact with thrust wakes generated by a robotic mechanism that produces a fish-like wake. We show that trout swim in thrust wakes, reduce their tail-beat frequencies, and synchronize with the robotic flapping mechanism. Our flow and pressure field analysis revealed that the trout are interacting with oncoming vortices and that they exhibit reduced pressure drag at the head compared to swimming in isolation. Together, these experiments suggest that trout swim energetically more efficiently in thrust wakes and support the hypothesis that swimming in the wake of one another is an advantageous strategy to save energy in a school.

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

An inertial mechanism behind dynamic station holding by fish swinging in a vortex street

Many aquatic and aerial animal species are known to utilise their surrounding flow field and/or the induced flow field of a neighbour to reduce their physical exertion, however, the mechanism by which such benefits are obtained has remained elusive. In this work, we investigate the swimming dynamics of rainbow trout in the wake of a thrust-producing oscillating hydrofoil. Despite the higher flow velocities in the inner region of the vortex street, some fish maintain position in this region, while exhibiting an altered swimming gait. Estimates of energy expenditure indicate a reduction in the propulsive cost when compared to regular swimming. By examining the accelerations of the fish, an explanation of the mechanism by which energy is harvested from the vortices is proposed. Similar to dynamic soaring employed by albatross, the mechanism can be linked to the non-equilibrium hydrodynamic forces produced when fish encounter the cross-flow velocity generated by the vortex street.

Fish swimming efficiency

Every spring a 600 lb Atlantic bluefin tuna travels over 3000 miles from Newfoundland to its spawning grounds in the Gulf of Mexico. That it does so on a meal of a couple of bluefish is nothing short of remarkable. Humans will likely never engineer such an efficient swimming machine. Of course, that has not stopped us from trying. We have achieved remarkable progress by following a strategy of inspiration by nature. At the same time, our fish-like robots often fall short of matching fish performance by a considerable margin. Despite our advances, we are still left asking the question: How do fish swim so well?

Hydrodynamic model of fish orientation in a channel flow

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.

One fascinating and perplexing fact about fish is that they tend to orient themselves and swim against the flow, rather than with it. This phenomenon is called rheotaxis, and it has countless examples, from salmon migrating upstream to lay their eggs to trout drift-foraging in a current. Yet, despite over a century of experimental studies, the mechanisms underlying rheotaxis remain poorly understood. There is general consensus that fish rely on water- and body-motion cues to vision, vestibular, tactile, and other senses. However, several questions remain unanswered, including how blind fish can perform rheotaxis or whether a passive hydrodynamic mechanism can support the phenomenon. One aspect that has been overlooked in studies of rheotaxis is the bidirectional hydrodynamic interaction between the fish and the surrounding flow, that is, how the presence of the fish alters the flow, which, in turn, affects the fish.

To address these open questions about rheotaxis, Porfiri, Zhang and Peterson wanted to develop a mathematical model of fish swimming, one that could help understand the passive hydrodynamic pathway that leads to swimming against a flow. Unlike experiments on live animals, a mathematical model offers the ability to remove cues to certain senses without interfering with animal behavior.

Porfiri, Zhang and Peterson modeled a fish as a pair of vortices located infinitely close to each other, rotating in opposite directions with the same strength. The vortex pair could freely move through an infinitely long channel with an imposed background flow, devoid of all sensory information expect of that accessed through the lateral line. Analyzing the resulting system revealed that there is a critical speed for the background flow above which the fish successfully orients itself against the flow, resulting in rheotaxis. This critical speed depends on the width of the channel the fish is swimming in. Depriving the fish of sensory information received through the lateral line does not preclude rheotaxis, indicating that rheotaxis could emerge in a completely passive manner.

The finding that the critical speed for rheotaxis depends on channel width could improve the design of experiments studying the phenomenon, since this effect could confound experiments where fish are confined in narrow channels. In this vein, Porfiri, Zhang and Peterson’s model could assist biologists in designing experiments detailing the multisensory nature of rheotaxis. Evidence of the importance of bidirectional hydrodynamic interactions on fish orientation may also inform modeling research on fish behavior.

Fish-inspired segment models for undulatory steady swimming

Many aquatic animals swim by undulatory body movements and understanding the diversity of these movements could unlock the potential for designing better underwater robots. Here, we analyzed the steady swimming kinematics of a diverse group of fish species to investigate whether their undulatory movements can be represented using a series of interconnected multi-segment models, and if so, to identify the key factors driving the segment configuration of the models. Our results show that the steady swimming kinematics of fishes can be described successfully using parsimonious models, 83% of which had fewer than five segments. In these models, the anterior segments were significantly longer than the posterior segments, and there was a direct link between segment configuration and swimming kinematics, body shape, and Reynolds number. The models representing eel-like fishes with elongated bodies and fishes swimming at high Reynolds numbers had more segments and less segment length variability along the body than the models representing other fishes. These fishes recruited their anterior bodies to a greater extent, initiating the undulatory wave more anteriorly. Two shape parameters, related to axial and overall body thickness, predicted segment configuration with moderate to high success rate. We found that head morphology was a good predictor of its segment length. While there was a large variation in head segments, the length of tail segments was similar across all models. Given that fishes exhibited variable caudal fin shapes, the consistency of tail segments could be a result of an evolutionary constraint tuned for high propulsive efficiency. The bio-inspired multi-segment models presented in this study highlight the key bending points along the body and can be used to decide on the placement of actuators in fish-inspired robots, to model hydrodynamic forces in theoretical and computational studies, or for predicting muscle activation patterns during swimming.

Universal Scaling Laws for Propulsive Performance of Thrust Producing Foils Undergoing Continuous or Intermittent Pitching

High efficiency thrust generating foils are extensively being researched for potential use as thrusters in micro air vehicles and biomimetic autonomous underwater vehicles. Here, we propose a simple reduced order model for prediction of thrust generation attributes of foils that are pitched either continuously or intermittently in a periodic and possibly asymmetric fashion. Our model accounts for the distinct thrust contributions from added mass, leading edge suction, quasi steady and wake terms, all deduced from a rigorous generalization of linearized potential theory to foils undergoing small amplitude multimodal flapping motion. Additionally, the model relies on Bone-Lighthill boundary layer thinning hypothesis to account for the pitching motion induced increase in the drag force exerted on the foil. We derive generic forms of the thrust coefficient for prescribed multimodal pitching motions and specifically in the limit of large reduced frequencies, demonstrate a convergence to rather simplified scaling laws that are functions of just the Reynolds number and Strouhal number based on root mean square of the foil’s trailing edge velocity. Comparisons with previously reported experimental and simulation-based investigations demonstrate that the scaling laws capture the influence of imposed pitch on thrust generation characteristics over a range of pitching waveforms ranging from sinusoidal to square or triangular-shaped waveforms and also waveforms corresponding to intermittent pitching. The generalized relations derived in our work and the asymptotic scaling laws deduced from them are applicable to a wide spectrum of self-propulsion enabling and thrust producing waveforms including the ones that can potentially be employed in burst and coast swimming.

Convergence of undulatory swimming kinematics across a diversity of fishes

Fishes exhibit an astounding diversity of locomotor behaviors from classic swimming with their body and fins to jumping, flying, walking, and burrowing. Fishes that use their body and caudal fin (BCF) during undulatory swimming have been traditionally divided into modes based on the length of the propulsive body wave and the ratio of head:tail oscillation amplitude: anguilliform, subcarangiform, carangiform, and thunniform. This classification was first proposed based on key morphological traits, such as body stiffness and elongation, to group fishes based on their expected swimming mechanics. Here, we present a comparative study of 44 diverse species quantifying the kinematics and morphology of BCF-swimming fishes. Our results reveal that most species we studied share similar oscillation amplitude during steady locomotion that can be modeled using a second-degree order polynomial. The length of the propulsive body wave was shorter for species classified as anguilliform and longer for those classified as thunniform, although substantial variability existed both within and among species. Moreover, there was no decrease in head:tail amplitude from the anguilliform to thunniform mode of locomotion as we expected from the traditional classification. While the expected swimming modes correlated with morphological traits, they did not accurately represent the kinematics of BCF locomotion. These results indicate that even fish species differing as substantially in morphology as tuna and eel exhibit statistically similar two-dimensional midline kinematics and point toward unifying locomotor hydrodynamic mechanisms that can serve as the basis for understanding aquatic locomotion and controlling biomimetic aquatic robots.

The performance of a flapping foil for a self-propelled fishlike body

Several fish species propel by oscillating the tail, while the remaining part of the body essentially contributes to the overall drag. Since in this case thrust and drag are in a way separable, most attention was focused on the study of propulsive efficiency for flapping foils under a prescribed stream. We claim here that the swimming performance should be evaluated, as for undulating fish whose drag and thrust are severely entangled, by turning to self-propelled locomotion to find the proper speed and the cost of transport for a given fishlike body. As a major finding, the minimum value of this quantity corresponds to a locomotion speed in a range markedly different from the one associated with the optimal efficiency of the propulsor. A large value of the feathering parameter characterizes the minimum cost of transport while the optimal efficiency is related to a large effective angle of attack. We adopt here a simple two-dimensional model for both inviscid and viscous flows to proof the above statements in the case of self-propelled axial swimming. We believe that such an easy approach gives a way for a direct extension to fully free swimming and to real-life configurations.

Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance

Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. Their bell morphology and relatively simple nervous systems make them attractive to robotocists. Although, the science community has devoted much attention to understanding their swimming performance, there is still much to be learned about the jet propulsive locomotive gait displayed by prolate jellyfish. Traditionally, computational scientists have assumed uniform duty cycle kinematics when computationally modeling jellyfish locomotion. In this study we used fluid-structure interaction modeling to determine possible enhancements in performance from shuffling different duty cycles together across multiple Reynolds numbers and contraction frequencies. Increases in speed and reductions in cost of transport were observed as high as 80% and 50%, respectively. Generally, the net effects were greater for cases involving lower contraction frequencies. Overall, robust duty cycle combinations were determined that led to enhanced or impeded performance.

Biorobotic insights into neuromechanical coordination of undulatory swimming

Skin sensors on an eel-like robot couple external hydrodynamic pressure with internal neural patterns for robust swimming.

High-Efficiency Can Be Achieved for Non-Uniformly Flexible Pitching Hydrofoils via Tailored Collective Interactions

New experiments examine the interactions between a pair of three-dimensional (AR = 2) non-uniformly flexible pitching hydrofoils through force and efficiency measurements. It is discovered that the collective efficiency is improved when the follower foil has a nearly out-of-phase synchronization with the leader and is located directly downstream with an optimal streamwise spacing of X*=0.5. The collective efficiency is further improved when the follower operates with a nominal amplitude of motion that is 36% larger than the leader’s amplitude. A slight degradation in the collective efficiency was measured when the follower was slightly-staggered from the in-line arrangement where direct vortex impingement is expected. Operating at the optimal conditions, the measured collective efficiency and thrust are ηC=62% and CT,C=0.44, which are substantial improvements over the efficiency and thrust of ηC=29% and CT,C=0.16 of two fully-rigid foils in isolation. This demonstrates the promise of achieving high-efficiency with simple purely pitching mechanical systems and paves the way for the design of high-efficiency bio-inspired underwater vehicles.

Automatic segmentation of fish midlines for optimizing robot design

While fish use continuous and flexible bodies to propel themselves, fish robots are often made from interconnected segments. How many segments do robots need to represent fish movements accurately? We propose a new method to automatically determine parsimonious robot models from actual fish data. We first identify key bending points (i.e., joint positions) along the body and then study the concerted movement of the segments so that the difference between actual fish and modelled bending kinematics is minimized. To demonstrate the utility of our method, we analyse the steady swimming kinematics of 10 morphologically distinct fish species. Broadly classified as sub-carangiform (e.g., rainbow trout) and carangiform (e.g., crevalle jack) swimmers, these species exhibit variations in the way they undulate when traditional parameters (including head and tail beat amplitudes, body wavelength and maximum curvature along the body) are considered. We show that five segments are sufficient to describe the kinematics with at least 99% accuracy. For optimal performance, segments should progressively get shorter towards the tail. We also show that locations where bending moments are applied vary among species, possibly because of differences in morphology. More specifically, we find that wider fish have shorter head segments. We discover that once bending points are factored in, the kinematics differences observed in these species collapse into a single undulatory pattern. The amplitude and timing of how body segments move entirely depend on their respective joint positions along the body. Head and body segments are also coupled in a timely manner, which depends on the position of the most anterior joint. Our findings provide a mechanistic understanding of how morphology relates to kinematics and highlight the importance of head control, which is often overlooked in current robot designs.

Tuna robotics: hydrodynamics of rapid linear accelerations

Fish routinely accelerate during locomotor manoeuvres, yet little is known about the dynamics of acceleration performance. Thunniform fish use their lunate caudal fin to generate lift-based thrust during steady swimming, but the lift is limited during acceleration from rest because required oncoming flows are slow. To investigate what other thrust-generating mechanisms occur during this behaviour, we used the robotic system termed Tunabot Flex, which is a research platform featuring yellowfin tuna-inspired body and tail profiles. We generated linear accelerations from rest of various magnitudes (maximum acceleration of [Formula: see text] at [Formula: see text] tail beat frequency) and recorded instantaneous electrical power consumption. Using particle image velocimetry data, we quantified body kinematics and flow patterns to then compute surface pressures, thrust forces and mechanical power output along the body through time. We found that the head generates net drag and that the posterior body generates significant thrust, which reveals an additional propulsion mechanism to the lift-based caudal fin in this thunniform swimmer during linear accelerations from rest. Studying fish acceleration performance with an experimental platform capable of simultaneously measuring electrical power consumption, kinematics, fluid flow and mechanical power output provides a new opportunity to understand unsteady locomotor behaviours in both fishes and bioinspired aquatic robotic systems.

Decoding the Relationships between Body Shape, Tail Beat Frequency, and Stability for Swimming Fish

As fish swim through a fluid environment, they must actively use their fins in concert to stabilize their motion and have a robust form of locomotion. However, there is little knowledge of how these forces act on the fish body. In this study, we employ a 3D immersed boundary model to decode the relationship between roll, pitch, and yaw of the fish body and the driving forces acting on flexible fish bodies. Using bluegill sunfish as our representative geometry, we first examine the role of an actuating torque on the stability of the fish model, with a torque applied at the head of the unconstrained fish body. The resulting kinematics is a product of the passive elasticity, fluid forces, and driving torque. We then examine a constrained model to understand the role that fin geometry, body elasticity, and frequency play on the range of corrective forces acting on the fish. We find non-monotonic behavior with respect to frequency, suggesting that the effective flexibility of the fins play an important role in the swimming performance.

How zebrafish turn: analysis of pressure force dynamics and mechanical work

Whereas many fishes swim steadily, zebrafish regularly exhibit unsteady burst-and-coast swimming, which is characterized by repeated sequences of turns followed by gliding periods. Such a behavior offers the opportunity to investigate the hypothesis that negative mechanical work occurs in posterior regions of the body during early phases of the turn near the time of maximal body curvature. Here, we used a modified particle image velocimetry (PIV) technique to obtain high-resolution flow fields around the zebrafish body during turns. Using detailed swimming kinematics coupled with body surface pressure computations, we estimated fluid-structure interaction forces and the pattern of forces and torques along the body during turning. We then calculated the mechanical work done by each body segment. We used estimated patterns of positive and negative work along the body to evaluate the hypothesis (based on fish midline kinematics) that the posterior body region would experience predominantly negative work. Between 10% and 20% of the total mechanical work was done by the fluid on the body (negative work), and negative work was concentrated in the anterior and middle areas of the body, not along the caudal region. Energetic costs of turning were calculated by considering the sum of positive and negative work and were compared with previous metabolic estimates of turning energetics in fishes. The analytical workflow presented here provides a rigorous way to quantify hydrodynamic mechanisms of fish locomotion and facilitates the understanding of how body kinematics generate locomotor forces in freely swimming fishes.