Speed limits on swimming of fishes and cetaceans

Scaling the tail beat frequency and swimming speed in underwater undulatory swimming

Undulatory swimming is the predominant form of locomotion in aquatic vertebrates. A myriad of animals of different species and sizes oscillate their bodies to propel themselves in aquatic environments with swimming speed scaling as the product of the animal length by the oscillation frequency. Although frequency tuning is the primary means by which a swimmer selects its speed, there is no consensus on the mechanisms involved. In this article, we propose scaling laws for undulatory swimmers that relate oscillation frequency to length by taking into account both the biological characteristics of the muscles and the interaction of the moving swimmer with its environment. Results are supported by an extensive literature review including approximately 1200 individuals of different species, sizes and swimming environments. We highlight a crossover in size around 0.5-1 m. Below this value, the frequency can be tuned between 2-20 Hz due to biological constraints and the interplay between slow and fast muscles. Above this value, the fluid-swimmer interaction must be taken into account and the frequency is inversely proportional to the length of the animal. This approach predicts a maximum swimming speed around 5-10 m.s-1 for large swimmers, consistent with the threshold to prevent bubble cavitation.

Spinosaurus is not an aquatic dinosaur

A predominantly fish-eating diet was envisioned for the sail-backed theropod dinosaur Spinosaurus aegyptiacus when its elongate jaws with subconical teeth were unearthed a century ago in Egypt. Recent discovery of the high-spined tail of that skeleton, however, led to a bolder conjecture that S. aegyptiacus was the first fully aquatic dinosaur. The 'aquatic hypothesis' posits that S. aegyptiacus was a slow quadruped on land but a capable pursuit predator in coastal waters, powered by an expanded tail. We test these functional claims with skeletal and flesh models of S. aegyptiacus. We assembled a CT-based skeletal reconstruction based on the fossils, to which we added internal air and muscle to create a posable flesh model. That model shows that on land S. aegyptiacus was bipedal and in deep water was an unstable, slow-surface swimmer (<1 m/s) too buoyant to dive. Living reptiles with similar spine-supported sails over trunk and tail are used for display rather than aquatic propulsion, and nearly all extant secondary swimmers have reduced limbs and fleshy tail flukes. New fossils also show that Spinosaurus ranged far inland. Two stages are clarified in the evolution of Spinosaurus, which is best understood as a semiaquatic bipedal ambush piscivore that frequented the margins of coastal and inland waterways.

The allometry of locomotion

Organismal locomotion mediates ecological interactions and shapes community dynamics. Locomotion is constrained by intrinsic and environmental factors and integrating these factors should clarify how locomotion affects ecology across scales. We extended general theory based on metabolic scaling and biomechanics to predict the scaling of five locomotor performance traits: routine speed, maximum speed, maximum acceleration, minimum powered turn radius, and angular speed. To test these predictions, we used phylogenetically informed analyses of a new database with 884 species and found support for our quantitative predictions. Larger organisms were faster but less maneuverable than smaller organisms. Routine and maximum speeds scaled with body mass to 0.20 and 0.17 powers, respectively, and plateaued at higher body masses, especially for maximum speed. Acceleration was unaffected by body mass. Minimum turn radius scaled to a 0.19 power, and the 95% CI included our theoretical prediction, as we predicted. Maximum angular speed scaled higher than predicted but in the same direction. We observed universal scaling among locomotor modes for routine and maximum speeds but the intercepts varied; flying organisms were faster than those that swam or ran. Acceleration was independent of size in flying and aquatic taxa but decreased with body mass in land animals, possibly due to the risk of injury large, terrestrial organisms face at high speeds and accelerations. Terrestrial mammals inhabiting structurally simple habitats tended to be faster than those in complex habitats. Despite effects of body size, locomotor mode, and habitat complexity, universal scaling of locomotory performance reveals the general ways organisms move across Earth's complex environments.

Centre-of-mass and minimal speed limits of the great hammerhead

The great hammerhead is denser than water, and hence relies on hydrodynamic lift to compensate for its lack of buoyancy, and on hydrodynamic moment to compensate for a possible misalignment between centres of mass and buoyancy. Because hydrodynamic forces scale with the swimming speed squared, whereas buoyancy and gravity are independent of it, there is a critical speed below which the shark cannot generate enough lift to counteract gravity, and there are anterior and posterior centre-of-mass limits beyond which the shark cannot generate enough pitching moment to counteract the buoyancy-gravity couple. The speed and centre-of-mass limits were found from numerous wind-tunnel experiments on a scaled model of the shark. In particular, it was shown that the margin between the anterior and posterior centre-of-mass limits is a few tenths of the product between the length of the shark and the ratio between its weight in and out of water; a diminutive 1% body length. The paper presents the wind-tunnel experiments, and discusses the roles that the cephalofoil and the pectoral and caudal fins play in longitudinal balance of a shark.

Energetic and physical limitations on the breaching performance of large whales

The considerable power needed for large whales to leap out of the water may represent the single most expensive burst maneuver found in nature. However, the mechanics and energetic costs associated with the breaching behaviors of large whales remain poorly understood. In this study we deployed whale-borne tags to measure the kinematics of breaching to test the hypothesis that these spectacular aerial displays are metabolically expensive. We found that breaching whales use variable underwater trajectories, and that high-emergence breaches are faster and require more energy than predatory lunges. The most expensive breaches approach the upper limits of vertebrate muscle performance, and the energetic cost of breaching is high enough that repeated breaching events may serve as honest signaling of body condition. Furthermore, the confluence of muscle contractile properties, hydrodynamics, and the high speeds required likely impose an upper limit to the body size and effectiveness of breaching whales.

Advantages of aquatic animals as models for bio-inspired drones over present AUV technology

Robotic systems are becoming more ubiquitous, whether on land, in the air, or in water. In the aquatic realm, aquatic drones including ROVs (remotely operated vehicles) and AUVs (autonomous underwater vehicles) have opened new opportunities to investigate the ocean depths. However, these technologies have limitations related to shipboard support, programing, and functionality in complex marine environments. A new form of AUV is being developed to become operational. These drones are based on animal designs and capabilities. Biological AUVs (BAUVs) promise to improve performance in the varied environments of the ocean. Comparison of animal swimming performance with conventional AUVs and BAUVs demonstrates that natural systems still have swimming capabilities beyond the current state of AUV technology. However, the performances of aquatic animals with respect to swimming speed, efficiency, maneuverability, and stealth can serve as benchmarks to direct the development of bio-inspired AUV technology with enhanced capabilities.

Jet direction in bubble collapse within rectangular and triangular channels

A vapor bubble collapsing near a solid boundary in a liquid produces a liquid jet that points toward the boundary. The direction of this jet has been studied for boundaries such as flat planes and parallel walls enclosing a channel. Extending these investigations to enclosed polygonal boundaries, we experimentally measure jet direction for collapsing bubbles inside a square and an equilateral triangular channel. Following the method of Tagawa and Peters [Phys. Rev. Fluids 3, 081601 (2018)10.1103/PhysRevFluids.3.081601] for predicting the jet direction in corners, we model the bubble as a sink in a potential flow and demonstrate by experiment that analytical solutions accurately predict jet direction within an equilateral triangle and square. We further use the method to develop predictions for several other polygons, specifically, a rectangle, an isosceles right triangle, and a 30^{∘}-60^{∘}-90^{∘} right triangle.

Unveiling the physical mechanism behind pistol shrimp cavitation

Snapping shrimps use a special shaped claw to generate a cavitating high speed water jet. Cavitation formed in this way, may be used for hunting/stunning prey and communication. The present work is a novel computational effort to provide insight on the mechanisms of cavitation formation during the claw closure. The geometry of the claw used here is a simplified claw model, based on prior experimental work. Techniques, such as Immersed Boundary and Homogenous Equilibrium Model (HEM), are employed to describe the claw motion and cavitating flow field respectively. The simulation methodology has been validated against prior experimental work and is applied here for claw closure at realistic conditions. Simulations show that during claw closure, a high velocity jet forms, inducing vortex roll-up around it. If the closure speed is high enough, the intensity of the swirling motion is enough to produce strong depressurization in the vortex core, leading to the formation of a cavitation ring. The cavitation ring moves along the jet axis and, soon after its formation, collapses and rebounds, producing high pressure pulses.

Regional endothermy as a trigger for gigantism in some extinct macropredatory sharks

Otodontids include some of the largest macropredatory sharks that ever lived, the most extreme case being Otodus (Megaselachus) megalodon. The reasons underlying their gigantism, distribution patterns and extinction have been classically linked with climatic factors and the evolution, radiation and migrations of cetaceans during the Paleogene. However, most of these previous proposals are based on the idea of otodontids as ectothermic sharks regardless of the ecological, energetic and body size constraints that this implies. Interestingly, a few recent studies have suggested the possible existence of endothermy in these sharks thus opening the door to a series of new interpretations. Accordingly, this work proposes that regional endothermy was present in otodontids and some closely related taxa (cretoxyrhinids), playing an important role in the evolution of gigantism and in allowing an active mode of live. The existence of regional endothermy in these groups is supported here by three different approaches including isotopic-based approximations, swimming speed inferences and the application of a novel methodology for assessing energetic budget and cost of swimming in extinct taxa. In addition, this finding has wider implications. It calls into question some previous paleotemperature estimates based partially on these taxa, suggests that the existing hypothesis about the evolution of regional endothermy in fishes requires modification, and provides key evidence for understanding the evolution of gigantism in active macropredators.

Determining forward speed from accelerometer jiggle in aquatic environments

How fast animals move is critical to understanding their energetic requirements, locomotor capacity, and foraging performance, yet current methods for measuring speed via animal-attached devices are not universally applicable. Here we present and evaluate a new method that relates forward speed to the stochastic motion of biologging devices since tag jiggle, the amplitude of the tag vibrations as measured by high sample rate accelerometers, increases exponentially with increasing speed. We successfully tested this method in a flow tank using two types of biologging devices and tested the method in situ on wild cetaceans spanning ∼3 to &gt;20 m in length using two types of suction cup-attached and two types of dart-attached tag. This technique provides some advantages over other approaches for determining speed as it is device-orientation independent and relies only on a pressure sensor and a high sample rate accelerometer, sensors that are nearly universal across biologging device types.

Maximum swimming speeds of sailfish and three other large marine predatory fish species based on muscle contraction time and stride length: a myth revisited

Billfishes are considered to be among the fastest swimmers in the oceans. Previous studies have estimated maximum speed of sailfish and black marlin at around 35 m s⁻¹ but theoretical work on cavitation predicts that such extreme speed is unlikely. Here we investigated maximum speed of sailfish, and three other large marine pelagic predatory fish species, by measuring the twitch contraction time of anaerobic swimming muscle. The highest estimated maximum swimming speeds were found in sailfish (8.3±1.4 m s⁻¹), followed by barracuda (6.2±1.0 m s⁻¹), little tunny (5.6±0.2 m s⁻¹) and dorado (4.0±0.9 m s⁻¹); although size-corrected performance was highest in little tunny and lowest in sailfish. Contrary to previously reported estimates, our results suggest that sailfish are incapable of exceeding swimming speeds of 10-15 m s⁻¹, which corresponds to the speed at which cavitation is predicted to occur, with destructive consequences for fin tissues.

Summary: Using muscle contraction measurements, this work provides evidence that sailfish are most likely unable to reach the extremely high speeds claimed by previous research and popular articles.

Landmark-based Morphometric and Meristic Analysis of Serranidae

The landmark-based morphometric and meristic analysis of the kelp grouper (Epinephelus bruneus), red spotted grouper (E. akaara) and seven-banded grouper (E. septemfasciatus) were performed to compare the differentiation of overall body shape and structure. The measurements of the morphometric dimensions were observed in 25 parts (truss dimension: 16 parts; head part dimension: 9 parts) of 38 morphometric dimensions and also meristic differences observed in 3 parts (dorsal fin, anal fin and caudal fin) of 6 meristic counts (P < 0.05). Observed morphometric characteristics primarily involved in truss and head part dimension, kelp grouper have larger values in caudal part of truss dimension, kelp grouper, red spotted grouper and seven-banded grouper have similar values in pectoral part of truss dimension, in addition to, results of head part dimension showed that red spotted grouper have smaller values in overall dimensions (P < 0.05). As meristic characteristics, kelp grouper have more number of anal fin rays than other fish, red spotted grouper have more number of dorsal soft rays than other fish, and seven spotted grouper have more number of anal soft rays, and caudal fin rays than other fish (P < 0.05). Photographed under the x-ray, kelp grouper have the most curved vertebral column and largest swim bladder than other fishes (P < 0.05). Our results of this study confirmed that 3 subfamily fishes adequately can distinguish with external body shape, and we hope that the results of our study could be used to identify in Serranidae family as taxonomical parameters.

Optimal orientation in flows: providing a benchmark for animal movement strategies

Animal movements in air and water can be strongly affected by experienced flow. While various flow-orientation strategies have been proposed and observed, their performance in variable flow conditions remains unclear. We apply control theory to establish a benchmark for time-minimizing (optimal) orientation. We then define optimal orientation for movement in steady flow patterns and, using dynamic wind data, for short-distance mass movements of thrushes (Turdus sp.) and 6000 km non-stop migratory flights by great snipes, Gallinago media. Relative to the optimal benchmark, we assess the efficiency (travel speed) and reliability (success rate) of three generic orientation strategies: full compensation for lateral drift, vector orientation (single-heading movement) and goal orientation (continually heading towards the goal). Optimal orientation is characterized by detours to regions of high flow support, especially when flow speeds approach and exceed the animal's self-propelled speed. In strong predictable flow (short distance thrush flights), vector orientation adjusted to flow on departure is nearly optimal, whereas for unpredictable flow (inter-continental snipe flights), only goal orientation was near-optimally reliable and efficient. Optimal orientation provides a benchmark for assessing efficiency of responses to complex flow conditions, thereby offering insight into adaptive flow-orientation across taxa in the light of flow strength, predictability and navigation capacity.

Not So Fast: Swimming Behavior of Sailfish during Predator-Prey Interactions using High-Speed Video and Accelerometry

Billfishes are considered among the fastest swimmers in the oceans. Despite early estimates of extremely high speeds, more recent work showed that these predators (e.g., blue marlin) spend most of their time swimming slowly, rarely exceeding 2 m s(-1). Predator-prey interactions provide a context within which one may expect maximal speeds both by predators and prey. Beyond speed, however, an important component determining the outcome of predator-prey encounters is unsteady swimming (i.e., turning and accelerating). Although large predators are faster than their small prey, the latter show higher performance in unsteady swimming. To contrast the evading behaviors of their highly maneuverable prey, sailfish and other large aquatic predators possess morphological adaptations, such as elongated bills, which can be moved more rapidly than the whole body itself, facilitating capture of the prey. Therefore, it is an open question whether such supposedly very fast swimmers do use high-speed bursts when feeding on evasive prey, in addition to using their bill for slashing prey. Here, we measured the swimming behavior of sailfish by using high-frequency accelerometry and high-speed video observations during predator-prey interactions. These measurements allowed analyses of tail beat frequencies to estimate swimming speeds. Our results suggest that sailfish burst at speeds of about 7 m s(-1) and do not exceed swimming speeds of 10 m s(-1) during predator-prey interactions. These speeds are much lower than previous estimates. In addition, the oscillations of the bill during swimming with, and without, extension of the dorsal fin (i.e., the sail) were measured. We suggest that extension of the dorsal fin may allow sailfish to improve the control of the bill and minimize its yaw, hence preventing disturbance of the prey. Therefore, sailfish, like other large predators, may rely mainly on accuracy of movement and the use of the extensions of their bodies, rather than resorting to top speeds when hunting evasive prey.

A probabilistic model for hydrokinetic turbine collision risks: exploring impacts on fish

A variety of hydrokinetic turbines are currently under development for power generation in rivers, tidal straits and ocean currents. Because some of these turbines are large, with rapidly moving rotor blades, the risk of collision with aquatic animals has been brought to attention. The behavior and fate of animals that approach such large hydrokinetic turbines have not yet been monitored at any detail. In this paper, we conduct a synthesis of the current knowledge and understanding of hydrokinetic turbine collision risks. The outcome is a generic fault tree based probabilistic model suitable for estimating population-level ecological risks. New video-based data on fish behavior in strong currents are provided and models describing fish avoidance behaviors are presented. The findings indicate low risk for small-sized fish. However, at large turbines (≥5 m), bigger fish seem to have high probability of collision, mostly because rotor detection and avoidance is difficult in low visibility. Risks can therefore be substantial for vulnerable populations of large-sized fish, which thrive in strong currents. The suggested collision risk model can be applied to different turbine designs and at a variety of locations as basis for case-specific risk assessments. The structure of the model facilitates successive model validation, refinement and application to other organism groups such as marine mammals.

Launching the AquaMAV: bioinspired design for aerial-aquatic robotic platforms

Current Micro Aerial Vehicles (MAVs) are greatly limited by being able to operate in air only. Designing multimodal MAVs that can fly effectively, dive into the water and retake flight would enable applications of distributed water quality monitoring, search and rescue operations and underwater exploration. While some can land on water, no technologies are available that allow them to both dive and fly, due to dramatic design trade-offs that have to be solved for movement in both air and water and due to the absence of high-power propulsion systems that would allow a transition from underwater to air. In nature, several animals have evolved design solutions that enable them to successfully transition between water and air, and move in both media. Examples include flying fish, flying squid, diving birds and diving insects. In this paper, we review the biological literature on these multimodal animals and abstract their underlying design principles in the perspective of building a robotic equivalent, the Aquatic Micro Air Vehicle (AquaMAV). Building on the inspire-abstract-implement bioinspired design paradigm, we identify key adaptations from nature and designs from robotics. Based on this evaluation we propose key design principles for the design of successful aerial-aquatic robots, i.e. using a plunge diving strategy for water entry, folding wings for diving efficiency, water jet propulsion for water takeoff and hydrophobic surfaces for water shedding and dry flight. Further, we demonstrate the feasibility of the water jet propulsion by building a proof-of-concept water jet propulsion mechanism with a mass of 2.6 g that can propel itself up to 4.8 m high, corresponding to 72 times its size. This propulsion mechanism can be used for AquaMAV but also for other robotic applications where high-power density is of use, such as for jumping and swimming robots.

How sailfish use their bills to capture schooling prey

The istiophorid family of billfishes is characterized by an extended rostrum or 'bill'. While various functions (e.g. foraging and hydrodynamic benefits) have been proposed for this structure, until now no study has directly investigated the mechanisms by which billfishes use their rostrum to feed on prey. Here, we present the first unequivocal evidence of how the bill is used by Atlantic sailfish (Istiophorus albicans) to attack schooling sardines in the open ocean. Using high-speed video-analysis, we show that (i) sailfish manage to insert their bill into sardine schools without eliciting an evasive response and (ii) subsequently use their bill to either tap on individual prey targets or to slash through the school with powerful lateral motions characterized by one of the highest accelerations ever recorded in an aquatic vertebrate. Our results demonstrate that the combination of stealth and rapid motion make the sailfish bill an extremely effective feeding adaptation for capturing schooling prey.

A physical model of the extreme mantis shrimp strike: kinematics and cavitation of Ninjabot

To study the mechanical principles and fluid dynamics of ultrafast power-amplified systems, we built Ninjabot, a physical model of the extremely fast mantis shrimp (Stomatopoda). Ninjabot rotates a to-scale appendage within the environmental conditions and close to the kinematic range of mantis shrimp's rotating strike. Ninjabot is an adjustable mechanism that can repeatedly vary independent properties relevant to fast aquatic motions to help isolate their individual effects. Despite exceeding the kinematics of previously published biomimetic jumpers and reaching speeds in excess of 25 m s(-1) at accelerations of 3.2 × 10(4) m s(-2), Ninjabot can still be outstripped by the fastest mantis shrimp, Gonodactylus smithii, measured for the first time in this study. G. smithii reached 30 m s(-1) at accelerations of 1.5 × 10(5) m s(-2). While mantis shrimp produce cavitation upon impact with their prey, they do not cavitate during the forward portion of their strike despite their extreme speeds. In order to determine how closely to match Ninjabot and mantis shrimp kinematics to capture this cavitation behavior, we used Ninjabot to produce strikes of varying kinematics and to measure cavitation presence or absence. Using Akaike Information Criterion to compare statistical models that correlated cavitation with a variety of kinematic properties, we found that in rotating and accelerating biological conditions, cavitation inception is best explained only by maximum linear velocity.

Exploring the mechanics of thunniform propulsion: a model study

Thunniform propulsion is considered a case study in convergent evolution. Independently derived at least four times, it is characterized by uniquely high lift-based thrust and efficient performance. As such, it has been the focus of studies from biologists, engineers, and physicists. Unfortunately, direct physical measurements of this phenomenon are difficult to obtain. Therefore, the majority of research so far has consisted of theoretical modeling or experimental testing with models of low biofidelity. We created a test apparatus that would more accurately mimic thunniform propulsion as seen in the skipjack tuna (Katsuwonus pelamis (L., 1758)). Motion parameters and swimming speeds, as well as caudal fin size, shape, and material properties, were all taken into account and closely matched with in vivo measurements. Instantaneous lateral and in-flow forces were measured in tests over a range of motion regimes. Overall, general motion parameter requirements for thrust generation were determined and quantified. Thrust production, of up to 0.42 N (per whole caudal fin) with a coefficient of thrust of approximately 0.2, were in line with estimates of whole-body drag. Propulsive efficiency estimates were low (≤35%) compared with estimates in the literature of up to 90%. Quasi-static analysis was also conducted and shown to underpredict measured thrust values by up to 50%.

Feeding requirements of white sharks may be higher than originally thought

Quantifying the energy requirements of animals in nature is critical for understanding physiological, behavioural, and ecosystem ecology; however, for difficult-to-study species such as large sharks, prey intake rates are largely unknown. Here, we use metabolic rates derived from swimming speed estimates to suggest that feeding requirements of the world's largest predatory fish, the white shark (Carcharodon carcharias), are several times higher than previously proposed. Further, our estimates of feeding frequency identify a clear benefit in seasonal selection of pinniped colonies - a white shark foraging strategy seen across much of their range.

Thresher sharks use tail-slaps as a hunting strategy

The hunting strategies of pelagic thresher sharks (Alopias pelagicus) were investigated at Pescador Island in the Philippines. It has long been suspected that thresher sharks hunt with their scythe-like tails but the kinematics associated with the behaviour in the wild are poorly understood. From 61 observations recorded by handheld underwater video camera between June and October 2010, 25 thresher shark shunting events were analysed. Thresher sharks employed tail-slaps to debilitate sardines at all times of day. Hunting events comprised preparation, strike, wind-down recovery and prey item collection phases, which occurred sequentially. Preparation phases were significantly longer than the others, presumably to enable a shark to windup a tail-slap. Tail-slaps were initiated by an adduction of the pectoral fins, a manoeuvre that changed a thresher shark's pitch promoting its posterior region to lift rapidly, and stall its approach. Tail-slaps occurred with such force that they may have caused dissolved gas to diffuse out of the water column forming bubbles. Thresher sharks were able to consume more than one sardine at a time, suggesting that tail-slapping is an effective foraging strategy for hunting schooling prey. Pelagic thresher sharks appear to pursue sardines opportunistically by day and night, which may make them vulnerable to fisheries. Alopiids possess specialist pectoral and caudal fins that are likely to have evolved, at least in part, for tail-slapping. The evidence is now clear; thresher sharks really do hunt with their tails.

Visual accommodation and active pursuit of prey underwater in a plunge-diving bird: the Australasian gannet

Australasian gannets (Morus serrator), like many other seabird species, locate pelagic prey from the air and perform rapid plunge dives for their capture. Prey are captured underwater either in the momentum (M) phase of the dive while descending through the water column, or the wing flapping (WF) phase while moving, using the wings for propulsion. Detection of prey from the air is clearly visually guided, but it remains unknown whether plunge diving birds also use vision in the underwater phase of the dive. Here we address the question of whether gannets are capable of visually accommodating in the transition from aerial to aquatic vision, and analyse underwater video footage for evidence that gannets use vision in the aquatic phases of hunting. Photokeratometry and infrared video photorefraction revealed that, immediately upon submergence of the head, gannet eyes accommodate and overcome the loss of greater than 45 D (dioptres) of corneal refractive power which occurs in the transition between air and water. Analyses of underwater video showed the highest prey capture rates during WF phase when gannets actively pursue individual fish, a behaviour that very likely involves visual guidance, following the transition after the plunge dive's M phase. This is to our knowledge the first demonstration of the capacity for visual accommodation underwater in a plunge diving bird while capturing submerged prey detected from the air.