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The heterogeneity of the physical environment determines the cost of transport for animals, shaping their energy landscape. Animals respond to this energy landscape by adjusting their distribution and movement to maximize gains and reduce costs. Much of our knowledge about energy landscape dynamics focuses on factors external to the animal, particularly the spatio-temporal variations of the environment. However, an animal's internal state can significantly impact its ability to perceive and utilize available energy, creating a distinction between the 'fundamental' and the 'realized' energy landscapes. Here, we show that the realized energy landscape varies along the ontogenetic axis. Locomotor and cognitive capabilities of individuals change over time, especially during the early life stages. We investigate the development of the realized energy landscape in the Central European Alpine population of the golden eagle Aquila chrysaetos, a large predator that requires negotiating the atmospheric environment to achieve energy-efficient soaring flight. We quantified weekly energy landscapes using environmental features for 55 juvenile golden eagles, demonstrating that energetic costs of traversing the landscape decreased with age. Consequently, the potentially flyable area within the Alpine region increased 2170-fold during their first three years of independence. Our work contributes to a predictive understanding of animal movement by presenting ontogeny as a mechanism shaping the realized energy landscape.
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Metabolismo Energético , Vuelo Animal , ÁguilasRESUMEN
AbstractMuscle-tendon unit (MTU) morphology and physiology are likely major determinants of locomotor performance and therefore Darwinian fitness. However, the relationships between underlying traits, performance, and fitness are complicated by phenomena such as coadaptation, multiple solutions, and trade-offs. Here, we leverage a long-running artificial selection experiment in which mice have been bred for high levels of voluntary running to explore MTU adaptation, as well as the role of coadaptation, multiple solutions, and trade-offs, in the evolution of endurance running. We compared the morphological and contractile properties of the triceps surae complex, a major locomotor MTU, in four replicate selected lines to those of the triceps surae complex in four replicate control lines. All selected lines have lighter and shorter muscles, longer tendons, and faster muscle twitch times than all control lines. Absolute and normalized maximum shortening velocities and contractile endurance vary across selected lines. Selected lines have similar or lower absolute velocities and higher endurance than control lines. However, normalized shortening velocities are both higher and lower in selected lines than in control lines. These findings potentially show an interesting coadaptation between muscle and tendon morphology and muscle physiology, highlight multiple solutions for increasing endurance running performance, demonstrate that a trade-off between muscle speed and endurance can arise in response to selection, and suggest that a novel physiology may sometimes allow this trade-off to be circumvented.
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Adaptación Fisiológica , Músculo Esquelético , Resistencia Física , Carrera , Tendones , Animales , Ratones , Carrera/fisiología , Tendones/fisiología , Resistencia Física/genética , Resistencia Física/fisiología , Músculo Esquelético/fisiología , Adaptación Fisiológica/fisiología , Evolución Biológica , Masculino , Femenino , Contracción Muscular/fisiologíaRESUMEN
PURPOSE: This study aimed to compare running economy across habituated and nonhabituated advanced footwear technology (AFT) in trained long-distance runners. METHODS: A total of 16 participants completed up to six 5-minute trials in 1 to 3 pairs of their own habituated shoes and 3 different and standardized AFTs at individual marathon pace. We measured oxygen uptake and carbon dioxide production and expressed running economy as oxygen uptake (in milliliters oxygen per kilogram per minute), oxygen cost of transport (oxygen per kilogram per minute), energetic cost (in watts per kilogram), and energetic cost of transport (in joules per kilogram per kilometer). We used linear mixed-effect models to evaluate differences. Relative shoe weight and shoe mileage (distance worn during running) were covariates. RESULTS: Forty-eight standardized and 29 individual AFT conditions were measured (mileage 117.0 [128.8] km, range 0-522 km; 25 habituated 135.7 [129.2] km, range 20-522 km; 4 nonhabituated 0 [0] km, range 0-0 km). Rating of perceived exertion, blood [La], and respiratory exchange ratio ranged from 9 to 15, 1.11 to 4.54 mmol/L, and 0.76 to 1.01. There was no effect for habituation on energetic cost of transport (thabituation = -.232, P = .409, b = -0.006; 95% CI, -0.058 to 0.046) or other running economy metrics. Neither shoe weight nor shoe mileage had an effect. CONCLUSIONS: Our results suggest that habituation to AFTs does not result in greater benefits in the use of AFTs. This means that implementation in training may not be needed, even if we cannot rule out any other possible benefits of habituation at this stage, such as adaptation of the musculoskeletal system.
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Metabolismo Energético , Consumo de Oxígeno , Zapatos , Humanos , Consumo de Oxígeno/fisiología , Masculino , Adulto , Femenino , Habituación Psicofisiológica/fisiología , Carrera de Maratón/fisiología , Dióxido de Carbono , Diseño de Equipo , Esfuerzo Físico/fisiología , Adulto Joven , Carrera/fisiologíaRESUMEN
Despite medical treatment focused on addressing walking disability, many millions of people with neurological conditions, like cerebral palsy (CP), struggle to maintain independent mobility. Lower limb exoskeletons and exosuits may hold potential for augmenting walking ability. However, it remains unknown whether these wearable robots are safe and beneficial for use outside of highly controlled laboratory environments, the demonstration of which is necessary for clinical translation. Here, we show that a lightweight, portable, ankle exoskeleton with an adaptable one-size-works-for-all assistance controller can improve energy efficiency and walking speed for individuals with CP spanning a wide spectrum of lower limb impairment in a multi-terrain real-world environment. Tested on an outdoor walking route with level, sloped, and stair terrain, robotic assistance resulted in a 15-18% (p = 0.013-0.026) reduction in estimated energy cost and a 7-8% (p = 0.001-0.004) increase in average walking speed across "shorter" 6-minute and "longer" 20-minute walking durations relative to unassisted walking. This study provides evidence that wearable robots may soon improve mobility in neighborhood, school, and community settings for individuals with CP.
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Successful performance in long distance race requires both high efficiency and stability. Previous research has demonstrated the high running efficiency of trained runners, but no prior study quantitatively addressed their orbital stability. In this study, we evaluated the efficiency and orbital stability of 8 professional long-distance runners and compared them with those of 8 novices. We calculated the cost of transport and normalized mechanical energy to assess physiological and mechanical running efficiency, respectively. We quantified orbital stability using Floquet Multipliers, which assess how fast a system converges to a limit cycle under perturbations. Our results show that professional runners run with significantly higher physiological and mechanical efficiency but with weaker orbital stability compared to novices. This finding is consistent with the inevitable trade-off between efficiency and stability; increase in orbital stability necessitates increase in energy dissipation. We suggest that professional runners have developed the ability to exploit inertia beneficially, enabling them to achieve higher efficiency partly at the cost of sacrificing orbital stability.
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BACKGROUND: Passive-dynamic ankle-foot orthoses (PD-AFOs) are often prescribed to address plantar flexor weakness during gait, which is commonly observed after stroke. However, limited evidence is available to inform the prescription guidelines of PD-AFO bending stiffness. This study assessed the extent to which PD-AFOs customized to match an individual's level of plantar flexor weakness influence walking function, as compared to No AFO and their standard of care (SOC) AFO. METHODS: Mechanical cost-of-transport, self-selected walking speed, and key biomechanical variables were measured while individuals greater than six months post-stroke walked with No AFO, with their SOC AFO, and with a stiffness-customized PD-AFO. Outcomes were compared across these conditions using a repeated measures ANOVA or Friedman test (depending on normality) for group-level analysis and simulation modeling analysis for individual-level analysis. RESULTS: Twenty participants completed study activities. Mechanical cost-of-transport and self-selected walking speed improved with the stiffness-customized PD-AFOs compared to No AFO and SOC AFO. However, this did not result in a consistent improvement in other biomechanical variables toward typical values. In line with the heterogeneous nature of the post-stroke population, the response to the PD-AFO was highly variable. CONCLUSIONS: Stiffness-customized PD-AFOs can improve the mechanical cost-of-transport and self-selected walking speed in many individuals post-stroke, as compared to No AFO and participants' standard of care AFO. This work provides initial efficacy data for stiffness-customized PD-AFOs in individuals post-stroke and lays the foundation for future studies to enable consistently effective prescription of PD-AFOs for patients post-stroke in clinical practice. TRIAL REGISTRATION: NCT04619043.
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Ortesis del Pié , Rehabilitación de Accidente Cerebrovascular , Velocidad al Caminar , Humanos , Masculino , Femenino , Persona de Mediana Edad , Rehabilitación de Accidente Cerebrovascular/instrumentación , Rehabilitación de Accidente Cerebrovascular/métodos , Velocidad al Caminar/fisiología , Anciano , Fenómenos Biomecánicos , Accidente Cerebrovascular/complicaciones , Accidente Cerebrovascular/fisiopatología , Tobillo/fisiología , Caminata/fisiología , Trastornos Neurológicos de la Marcha/rehabilitación , Trastornos Neurológicos de la Marcha/etiologíaRESUMEN
The human foot's arch is thought to be beneficial for efficient gait. This study addresses the extent to which arch stiffness changes alter the metabolic energy requirements of human gait. Computational musculoskeletal simulations of steady state walking using direct collocation were performed. Across a range of foot arch stiffnesses, the metabolic cost of transport decreased by less than 1% with increasing foot arch stiffness. Increasing arch stiffness increased the metabolic efficiency of the triceps surae during push-off, but these changes were almost entirely offset by other muscle groups consuming more energy with increasing foot arch stiffness.
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Climbing animals theoretically should optimize the energetic costs of vertical climbing while also maintaining stability. Many modifications to climbing behaviors have been proposed as methods of satisfying these criteria, focusing on controlling the center of mass (COM) during ascent. However, the link between COM movements and metabolic energy costs has yet to be evaluated empirically. In this study, we manipulated climbing conditions across three experimental setups to elicit changes in COM position, and measured the impact of these changes upon metabolic costs across a sample of 14 humans. Metabolic energy was assessed via open flow respirometry, while COM movements were tracked both automatically and manually. Our findings demonstrate that, despite inducing variation in COM position, the energetic costs of climbing remained consistent across all three setups. Differences in energetic costs were similarly not affected by body mass; however, velocity had a significant impact upon both cost of transport and cost of locomotion, but such a relationship disappeared when accounting for metabolic costs per stride. These findings suggest that climbing has inescapable metabolic demands driven by gaining height, and that attempts to mitigate such a cost, with perhaps the exception of increasing speed, have only minimal impacts. We also demonstrate that metabolic and mechanical energy costs are largely uncorrelated. Collectively, we argue that these data refute the idea that efficient locomotion is the primary aim during climbing. Instead, adaptations towards effective climbing should focus on stability and reducing the risk of falling, as opposed to enhancing the metabolic efficiency of locomotion.
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Metabolismo Energético , Humanos , Masculino , Adulto , Femenino , Fenómenos Biomecánicos , Locomoción/fisiología , Adulto Joven , Marcha/fisiologíaRESUMEN
The balance between energetic costs and acquisition in free-ranging species is essential for survival, and provides important insights regarding the physiological impact of anthropogenic disturbances on wild animals. For marine mammals such as beluga whales (Delphinapterus leucas), the first step in modeling this bioenergetic balance requires an examination of resting and active metabolic demands. Here, we used open-flow respirometry to measure oxygen consumption during surface rest and submerged swimming by trained beluga whales, and compared these measurements with those of a commonly studied odontocete, the Atlantic bottlenose dolphin (Tursiops truncatus). Both resting metabolic rate (3012±126.0â kJâ h-1) and total cost of transport (1.4±0.1â Jâ kg-1 m-1) of beluga whales were consistent with predicted values for moderately sized marine mammals in temperate to cold-water environments, including dolphins measured in the present study. By coupling the rate of oxygen consumption during submerged swimming with locomotor metrics from animal-borne accelerometer tags, we developed predictive relationships for assessing energetic costs from swim speed, stroke rate and partial dynamic acceleration. Combining these energetic data with calculated aerobic dive limits for beluga whales (8.8â min), we found that high-speed responses to disturbance markedly reduce the whale's capacity for prolonged submergence, pushing the cetaceans to costly anaerobic performances that require prolonged recovery periods. Together, these species-specific energetic measurements for beluga whales provide two important metrics, gait-related locomotor costs and aerobic capacity limits, for identifying relative levels of physiological vulnerability to anthropogenic disturbances that have become increasingly pervasive in their Arctic habitats.
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Ballena Beluga , Delfín Mular , Caniformia , Buceo , Animales , Natación , Consumo de Oxígeno , CetáceosRESUMEN
Stream and river ecosystems present fluvial fishes with a dynamic energy landscape because moving water generates heterogeneous flow fields that are rarely static in space and time. Fish movement behavior should be consistent with conserving energy in these dynamic flowing environments, but little evidence supporting this hypothesis exists. Here, we tested experimentally whether three general movement behaviors-against the current, with the current, or holding position (i.e., staying in one position and location)-were performed in a way consistent with minimizing the cost of swimming in a heterogeneous flow field. We tested the effects of water velocity on movement behavior across three age classes (0, 1, and 5 years) of two different fluvial specialist fishes, the pallid sturgeon (Scaphirhynchus albus) and shovelnose sturgeon (Scaphirhynchus platorynchus). Individuals from the three age classes were exposed to a continuous and dynamic velocity field ranging from 0.02 to 0.53 m s-1, which represented natural benthic flow regimes occupied by these species in rivers. Both sturgeon species exhibited the same pattern with regard to their tendency to hold position, move upstream, or move downstream. Moving downstream was positively associated with velocity for all age groups. Moving upstream was inversely related to velocity for young fish, but as the fish aged, moving upstream was not related to water velocity. The oldest fish (age 5) moved upstream more frequently compared to the younger age classes. Holding position within a water current was the most frequent behavior and occurred with similar probability across the range of experimental velocity for youngest fish (age 0), but was inversely related to velocity in older fish. Our experiment across age classes suggests that the suite of swimming behaviors exhibited by fluvial specialists might have evolved to mitigate the energetic costs of complex energy landscapes generated by moving water to ultimately maximize net energy gain.
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Ecosistema , Peces , Animales , Ríos , NataciónRESUMEN
Autonomous robots are used to inspect, repair and maintain underwater assets. These tasks require energy-efficient robots, including efficient movement to extend available operational time. To examine the suitability of a propulsion system based on undulating fins, we built two robots with one and two fins, respectively, and conducted a parametric study for combinations of frequency, amplitude, wavenumber and fin shapes in free-swimming experiments, measuring steady-state swimming speed, power consumption and cost of transport. The following trends emerged for both robots. Swimming speed was more strongly affected by frequency than amplitude across the examined wavenumbers and fin heights. Power consumption was sensitive to frequency at low wavenumbers, and increasingly sensitive to amplitude at high wavenumbers. This increasing sensitivity of amplitude was more pronounced in tall rather than short fins. Cost of transport showed a complex relation with fin size and kinematics and changed drastically across the mapped parameter space. At equal fin kinematics as the single-finned robot, the double-finned robot swam slightly faster (>10%) with slightly lower power consumption (<20%) and cost of transport (<40%). Overall, the robots perform similarly to finned biological swimmers and other bio-inspired robots, but do not outperform robots with conventional propulsion systems.
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Metabolic cost minimization is thought to underscore the neural control of locomotion. Yet, avoiding high muscle activation, a cause of fatigue, often outperforms energy minimization in computational predictions of human gait. Discerning the relative importance of these criteria in human walking has proved elusive, in part, because they have not been empirically decoupled. Here, we explicitly decouple whole-body metabolic cost and 'fatigue-like' muscle activation costs (estimated from electromyography) by pitting them against one another using two distinct gait tasks. When experiencing these competing costs, participants (n = 10) chose the task that avoided overburdening muscles (fatigue avoidance) at the expense of higher metabolic power (p < 0.05). Muscle volume-normalized activation more closely models energy use and was also minimized by the participants' decision (p < 0.05), demonstrating that muscle activation was, at best, an inaccurate signal for metabolic energy. Energy minimization was only observed when there was no adverse effect on muscle activation costs. By decoupling whole-body metabolic and muscle activation costs, we provide among the first empirical evidence of humans embracing non-energetic optimality in favour of a clearly defined neuromuscular objective. This finding indicates that local muscle fatigue and effort may well be key factors dictating human walking behaviour and its evolution.
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Metabolismo Energético , Caminata , Humanos , Metabolismo Energético/fisiología , Caminata/fisiología , Marcha/fisiología , Locomoción/fisiología , Músculos , Fenómenos Biomecánicos/fisiología , Músculo Esquelético/fisiologíaRESUMEN
Predicted future warming of aquatic environments could make fish vulnerable to naturally occurring fasting periods during migration between feeding and spawning sites, as these endeavours become energetically more expensive. In this study, Atlantic salmon (Salmo salar) acclimated to midrange (9°C) or elevated suboptimal (18°C) temperatures were subjected to critical (Ucrit) and sustained (4 hours at 80% Ucrit) swimming trials before and after 4 weeks of fasting. Fasting caused weight losses of 7.3% and 8.3% at 9°C and 18°C, respectively. The Ucrit was unaffected by fasting, but higher at 18°C. Fatigue was associated with higher plasma cortisol, osmolality, Na+ and Cl- at 18°C, and ionic disturbances were higher in fasted fish. All fish completed the sustained swim trials while maintaining constant oxygen uptake rates (MO2), indicating strictly aerobic swimming efforts. At low swimming speeds MO2 was downregulated in fasted fish by 23.8% and 15.6% at 9°C and 18°C, respectively, likely as an adaptation to preserve resources. However, at higher speeds MO2 became similar to fed fish showing that maximum metabolic rates were maintained. The changes in MO2 lowered costs of transport and optimal swimming speeds in fasted fish at both temperatures, but these energetic alterations were smaller at 18°C while routine MO2 was 57% higher than at 9°C. As such, this study shows that Atlantic salmon maintain both glycolytic and aerobic swimming capacities after extended fasting, even at elevated suboptimal temperatures, and adaptive metabolic downregulation provides increased swimming efficiency in fasted fish. Although, improved swimming energetics were smaller when fasting at the higher temperature while metabolism becomes elevated. This could affect migration success in warming climates, especially when considering interactions with other costly activities such as coping with parasites obtained when passing aquaculture sites during seaward travel or gonad development while being voluntarily anorexic during upriver travel to spawning grounds.
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Human runners have long been thought to have the ability to consume a near-constant amount of energy per distance traveled, regardless of speed, allowing speed to be adapted to particular task demands with minimal energetic consequence.1-3 However, recent and more precise laboratory measures indicate that humans may in fact have an energy-optimal running speed.4-6 Here, we characterize runners' speeds in a free-living environment and determine if preferred speed is consistent with task- or energy-dependent objectives. We analyzed a large-scale dataset of free-living runners, which was collected via a commercial fitness tracking device, and found that individual runners preferred a particular speed that did not change across commonly run distances. We compared the data from lab experiments that measured participants' energy-optimal running speeds with the free-living preferred speeds of age- and gender-matched runners in our dataset and found the speeds to be indistinguishable. Human runners prefer a particular running speed that is independent of task distance and is consistent with the objective of minimizing energy expenditure. Our findings offer an insight into the biological objectives that shape human running preferences in the real world-an important consideration when examining human ecology or creating training strategies to improve performance and prevent injury.
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Carrera , Adaptación Fisiológica , Fenómenos Biomecánicos , Metabolismo Energético , Ejercicio Físico , Marcha , HumanosRESUMEN
This study combines metabolic and kinematic measurements at the whole-body level, with EMG and ultrasound measurements to investigate the influence of muscle-tendon mechanical behavior on the energy cost (Cnet ) of walking (from 2 to 8 km·h-1 ). Belly gearing (Gb = Δmuscle-belly length/Δfascicles length) and tendon gearing (Gt = ∆muscle-tendon unit length/∆muscle-belly length) of vastus lateralis (VL) and gastrocnemius medialis (GM) were calculated based on ultrasound data. Pendular energy recovery (%R) was calculated based on kinematic data, whereas the cumulative activity per distance travelled (CMAPD) was calculated for the VL, GM, tibialis anterior, and biceps femoris as the ratio between their EMG activity and walking speed. Finally, total CAMPD (CMAPDTOT ) was calculated as the sum of the CMAPD of all the investigate muscles. Cnet and CMAPDTOT showed a U-shaped behavior with a minimum at 4.2 and 4.1 km·h-1 , respectively; while %R, VL, and GM belly gearing showed an opposite trend, reaching a maximum (60% ± 5%, 1.1 ± 0.1 and 1.5 ± 0.1, respectively), between 4.7 and 5 km·h-1 . Gt was unaffected by speed in GM (3.5 ± 0.1) and decreased as a function of it in VL. A multiple stepwise linear regression indicated that %R has the greatest influence on Cnet, followed by CMAPDTOT and GM belly gearing. The role of Gb on Cnet could be attributed to its role in determining muscle work: when Gb increases, fascicles shortening decreases compared with that of the muscle-belly, thereby reducing the energy cost of contraction.
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Músculo Esquelético , Tendones , Fenómenos Biomecánicos , Electromiografía , Humanos , Músculo Esquelético/diagnóstico por imagen , Músculo Esquelético/fisiología , Tendones/diagnóstico por imagen , Tendones/fisiología , Ultrasonografía , CaminataRESUMEN
During the last decade, biomechanical and kinematic studies have suggested that a belly-dragging gait may have represented a critical locomotor stage during tetrapod evolution. This form of locomotion is hypothesized to facilitate animals to move on land with relatively weaker pectoral muscles. The Indonesian blue-tongued skink (Tiliqua gigas) is known for its belly-dragging locomotion and is thought to employ many of the same spatiotemporal gait characteristics of stem tetrapods. Conversely, the savannah monitor (Varanus exanthematicus) employs a raised quadrupedal gait. Thus, differences in the energetic efficiency of locomotion between these taxa may elucidate the role of energetic optimization in driving gait shifts in early tetrapods. Five Tiliqua and four Varanus were custom-fitted for 3D printed helmets that, combined with a Field Metabolic System, were used to collect open-flow respirometry data including O2 consumption, CO2 production, water vapor pressure, barometric pressure, room temperature, and airflow rates. Energetic data were collected for each species at rest, and when walking at three different speeds. Energetic consumption in each taxon increased at greater speeds. On a per-stride basis, energetic costs appear similar between taxa. However, significant differences were observed interspecifically in terms of net cost of transport. Overall, energy expenditure was ~20% higher in Tiliqua at equivalent speeds, suggesting that belly-dragging does impart a tangible energetic cost during quadrupedal locomotion. This cost, coupled with the other practical constraints of belly-dragging (e.g., restricting top-end speed and reducing maneuverability in complex terrains) may have contributed to the adoption of upright quadrupedal walking throughout tetrapod locomotor evolution.
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Marcha , Lagartos , Animales , Fenómenos Biomecánicos , Marcha/fisiología , Indonesia , Locomoción/fisiología , Caminata/fisiologíaRESUMEN
The energetic cost of walking varies with mass and speed; however, the metabolic cost of carrying loads has not consistently increased proportionally to the mass carried. The cost of carrying mass, and the speed at which human walkers carry this mass, has been shown to vary with load position and load description (e.g. child vs. groceries). Additionally, the preponderance of women carriers around the world, and the tendency for certain kinds of population-level sexual dimorphism has led to the hypothesis that women might be more effective carriers than men. Here, I investigate the energetic cost and speed changes of women (N = 9) and men (N = 6) walking through the woods carrying their own babies (mean baby mass = 10.6 kg) in three different positions - on their front, side and back using the same Ergo fabric baby sling. People carrying their babies on their backs are able to maintain their unloaded walking speed (1.4 m/s) and show the lowest increase in metabolic cost per distance (J/m, 17.4%). Women carry the babies for a lower energetic cost than men at all conditions (p < 0.01). Further energetic and kinematic evidence elucidates the preponderance of back-carrying cross-culturally, and illustrates the importance of relatively wider bi-trochanteric breadths for reducing the energetic costs of carrying.
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Energetic expenditure is an important factor in animal locomotion. Here we test the hypothesis that fishes control tail-beat kinematics to optimize energetic expenditure during undulatory swimming. We focus on two energetic indices used in swimming hydrodynamics, cost of transport and Froude efficiency. To rule out one index in favour of another, we use computational-fluid dynamics models to compare experimentally observed fish kinematics with predicted performance landscapes and identify energy-optimized kinematics for a carangiform swimmer, an anguilliform swimmer and larval fishes. By locating the areas in the predicted performance landscapes that are occupied by actual fishes, we found that fishes use combinations of tail-beat frequency and amplitude that minimize cost of transport. This energy-optimizing strategy also explains why fishes increase frequency rather than amplitude to swim faster, and why fishes swim within a narrow range of Strouhal numbers. By quantifying how undulatory-wave kinematics affect thrust, drag, and power, we explain why amplitude and frequency are not equivalent in speed control, and why Froude efficiency is not a reliable energetic indicator. These insights may inspire future research in aquatic organisms and bioinspired robotics using undulatory propulsion.