Thrust Production Research Articles

Torque, speed, and power requirements for the design of a lower limb exoskeleton to augment human finned swimming

Abstract The authors seek to design a lower limb exoskeleton to augment human finned swimming; however, data associated with human finned swimming previously did not exist, particularly data that characterizes the active joint torque requirements for human-scale finned swimming motion and the corresponding thrust generation. Since these data are not directly measurable nor easily computed in human subject experiments, the authors instead employed a human-scale robotic platform to characterize the relationship between joint torque, speed, power, and thrust production during flutter kick swimming, specifically at the hip joints. Among the useful insights from this study: (1) the underwater environment can be accurately modeled as a simple viscous load as seen by the hip joints, where viscous coefficient depends on the type of fin; (2) accordingly, for a given fin, movement at any amplitude and frequency is invariant when motion is normalized by amplitude; velocity and torque by the product of amplitude and frequency; and power and thrust by the square of the product of amplitude and frequency; (3) the power-specific thrust is invariant, regardless of fin type, amplitude of motion, and frequency of motion; and 4) the phasing between right and left legs does not have a significant effect on thrust generation (i.e., kicking in-phase and kicking in opposition behave similarly). The authors hope this data will be useful to other researchers interested in developing lower limb exoskeletons to augment underwater human finned swimming.

Unsteady CFD simulation of a rotor blade under various wind conditions

Wind and gusts can significantly impact the performance of rotors and turbines. The transient behavior of the rotor should be carefully examined to account for these effects. This paper investigates the unsteady aerodynamic characteristics of a rotor blade under different wind conditions, such as direction, speed, and angle. A 3D transient Computational Fluid Dynamics (CFD) simulation using the dynamic mesh technique is performed to analyze the rotor dynamics. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations with the k-ω SST turbulence model are solved. The rotor blade used for this study is the U15XXL Combo KV29 industrial blade, which has not been numerically analyzed before. The results show that wind in the same direction as the rotation reduces the thrust more than lateral or opposite wind. Lateral wind with a speed lower than 5 m/s decreases the blade performance, but higher speeds increase it. Higher lateral wind speeds also cause two peaks in the torque curve, forming a butterfly wing shape in the polar torque plot and multiple extrema in the torque curve with increasing speed. The maximum thrust shifts slightly to the left with increasing lateral wind speed. The lateral angle does not affect the average thrust produced in one blade revolution but only causes a spatial shift. The thrust production decreases as the angle approaches the opposite direction of rotation. The motion amplitude decreases, and the curve becomes smoother as this angle increases. A nearly straight line similar to no side wind is observed at 60 and 90 degrees, which is attributed to the constant effective angle of attack during the rotation cycle.

Unraveling hydrodynamic interactions in fish schools: A three-dimensional computational study of in-line and side-by-side configurations

We numerically investigate the hydrodynamic interactions between a pair of three-dimensional (3D) fish-like bodies arranged in both in-line and side-by-side configurations. The morphology and kinematics of these fish-like bodies are modeled on a live rainbow trout (Oncorhynchus mykiss) observed during steady swimming in the laboratory. An immersed-boundary-method-based incompressible Navier–Stokes flow solver is employed to capture the flow dynamics around the fish-like bodies accurately. Our findings indicate that hydrodynamic performance of individual fish in both arrangements is influenced by their spatial separation when in close proximity as well as by the relative phase difference between the two fish. In the case of in-phase in-line schools, the leading fish experiences up to 5.3% increase in propulsive efficiency, attributed to the water blockage effect caused by the following fish. In comparison, the following fish experiences an increase in drag and power consumption along its body. Detailed analysis reveals that this rise in drag primarily results from an increase in friction drag (89%), driven by the amplified velocity field around the fish's body. Furthermore, altering the phase difference between the fish can help reduce pressure drag on the following fish by affecting the interaction between incoming vortex rings and its trunk. In side-by-side schools with in-phase swimming, a reduction of 6.8% in power consumption on the caudal fin is achieved for each fish when the transverse distance is maintained at 0.25 body lengths. Flow analysis reveals that the decrease in power usage is attributed to a diminished velocity field between the caudal fins, facilitating flow separation and subsequently reducing energy expenditure required for generating comparative thrust. For the out-of-phase swimming, the side-by-side school system experiences enhanced thrust production, owing to a wake energy recapture mechanism. The degree of enhancement varies for each fish and is determined by the specific phase difference. These insights obtained from our study hold the potential to inform the design and navigation strategies of underwater robotic swarms.

A multi-fidelity approach for wind farm simulations and comparison with field data

The prediction of energy production and structural loads within wind farms is of high interest for wind industries to optimize the wind farm design and control under a variety of atmospheric conditions. However, it is still a key challenge to predict them accurately and efficiently due to the complex interactions between wind turbines and turbulent flows. Nowadays, high-fidelity simulations using Reynolds-Averaged Navier-Stokes (RANS) or Large-Eddy Simulation (LES) coupled with actuator disk or actuator line method are widely developed and used in wind farm analysis, but it still needs a huge computational resource, especially in the application of a commercial wind farm with large number of turbines. In this context, a mid-fidelity simulation tool based on the Dynamics Wake Meandering (DWM) model called FAST.Farm has been developed by National Renewable Energy Laboratory (NREL) in order to tackle this challenge. It allows to capture essential physics at the turbine scale as well as at the farm scale in a computational efficient manner. This study focuses on the calibration of DWM model which is the key to minimize inaccuracies between mid-fidelity and high-fidelity simulations regarding key performance indicators, e.g. thrust and power production. The calibration is made for DTU10MW wind turbine and shows a good improvement in accuracy compared to default parameters. The calibrated DWM model is finally employed to forecast the power generation for two turbines within a reference wind farm. A good improvement on the prediction is also obtained thanks to the calibrated parameters.

A thrust inversion method for small satellite electric propulsion based on a momentum wheel

Electric propulsion, which is an advanced form of thrust production, is widely used in small satellites. Measuring the thrust of electric propulsion in an orbit is difficult because it is very small (μN∼mN). However, the thrust of electric propulsion can be determined by evaluating the change in the speed of a momentum wheel. The contributions of this paper mainly include two aspects: 1) a robust PID controller and 2) a thrust inversion method. The torque of the electric propulsion is regarded as the disturbance torque in this paper. To achieve finite-time attitude stabilization of a satellite during electric propulsion, a robust PID controller is designed. Furthermore, the thrust of the electric propulsion can be determined in the stable attitude of the satellite by only measuring the speed derivative of the momentum wheel. Compared with the traditional thrust inversion method, the designed thrust inversion method is simple and effective and does not use a filtering algorithm. In the HIL experiment, the error rate between the inverted thrust (31.287 μN) and the designed thrust (30 μN) is 4.29%. Most importantly, the thrust inversion method is verified in orbit based on the small satellite APSCO SSS-1, which is consistent with the HIL experimental results and ground test results.

Operational mechanism of valved-pulsejet engines

The study investigates twelve configurations of the self-aspirated valved pulsejet, focusing on its operational mechanism. It begins by characterizing the engine's acoustic field with varied boundary conditions, revealing an extended effective acoustic length beyond the combustion chamber and tailpipe sections when the valve is open. Radial and lateral velocity fluctuations are hypothesized as causes for vortex structure generation. Analysis of reacting pulsejets using gasoline and ethanol fuels shows that the operating frequencies are unaffected by fuel type, with geometric arrangement as the primary frequency factor. Fluctuations in dynamic pressure, microphone readings, and thrust characterize engine stability, impacted by low-frequency modes and higher harmonics. Tailpipe length emerges as the key geometric factor for performance enhancement with the medium size being the optimal option. Pressure field analysis demonstrates shock wave generation during ignition, serving as an excitation mechanism. Notably, different configurations with varied operating frequencies can yield equivalent thrust, indicating that thrust production is not solely dependent on pressure rise during combustion, despite similar pressure rise observed across most cases.

The impact of the Laval nozzle shape on thrust production, using the method of characteristics

This investigation examines the influence of Laval nozzle geometry on thrust production using the method of characteristics. It explores various divergent section configurations, analyzing their impact on nozzle design and performance. Comparative analysis of software tools, study of supersonic flow phenomena, and application of the method of characteristics form the core of this research. Findings showcase strong agreement between computational tools, emphasizing the Mach number's role in divergent section shape variations and thrust force. Additionally, the study scrutinizes over-expansion and under-expansion phenomena, validated through computational simulations. Future research should be aimed at enhancing computational methodologies and investigating additional parameters affecting nozzle performance, promising advancements in rocket propulsion technology.

Thrust production and chordal flexion of the flukes of bottlenose dolphins performing tail stands at different efforts.

Dolphins have become famous for their ability to perform a wide variety of athletic and acrobatic behaviors including high-speed swimming, maneuverability, porpoising and tail stands. Tail stands are a behavior where part of the body is held vertically above the water's surface, achieved through thrust produced by horizontal tail fluke oscillations. Strong, efficient propulsors are needed to generate the force required to support the dolphin's body weight, exhibiting chordwise and spanwise flexibility throughout the stroke cycle. To determine how thrust production, fluke flexibility and tail stroke kinematics vary with effort, six adult bottlenose dolphins (Tursiops truncatus) were tested at three different levels based on the position of the center of mass (COM) relative to the water's surface: low (COM below surface), medium (COM at surface) and high (COM above surface) effort. Additionally, fluke flexibility was measured as a flex index (FI=chord length/camber length) at four points in the stroke cycle: center stroke up (CU), extreme top of stroke (ET), center stroke down (CD) and extreme bottom of stroke (EB). Video recordings were analyzed to determine the weight supported above the water (thrust production), peak-to-peak amplitude, stroke frequency and FI. Force production increased with low, medium and high efforts, respectively. Stroke frequency also increased with increased effort. Amplitude remained constant with a mean 33.8% of body length. Significant differences were seen in the FI during the stroke cycle. Changes in FI and stroke frequency allowed for increased force production with effort, and the peak-to-peak amplitude was higher compared with that for horizontal swimming.

Tailbeat perturbations improve swimming efficiency by reducing the phase lag between body motion and the resulting fluid response.

Understanding how animals swim efficiently and generate high thrust in complex fluid environments is of considerable interest to researchers in various fields, including biology, physics, and engineering. However, the influence of often-overlooked perturbations on swimming fish remains largely unexplored. Here, we investigate the propulsion generated by oscillating tailbeats with superimposed rhythmic perturbations of high frequency and low amplitude. We reveal, using a combination of experiments in a biomimetic fish-like robotic platform, computational fluid dynamics simulations, and theoretical analysis, that rhythmic perturbations can significantly increase both swimming efficiency and thrust production. The introduction of perturbations increases pressure-induced thrust, while reduced phase lag between body motion and the subsequent fluid dynamics response improves swimming efficiency. Moreover, our findings suggest that beneficial perturbations are sensitive to kinematic parameters, resolving previous conflicts regarding the effects of such perturbations. Our results highlight the potential benefits of introducing perturbations in propulsion generators, providing potential hypotheses for living systems and inspiring the design of artificial flapping-based propulsion systems.

High propulsive performance by an oscillating foil in a stratified fluid

We investigate numerically the propulsion characteristics of an oscillating foil undergoing coupled heave and pitch motion in a linearly density-stratified flow. A parameter space defined by the internal Froude number ( $1 \le Fr \le 10$ ) and the maximum angle of attack ( $5^\circ \le {\alpha _0} \le 30^\circ$ ) is considered in our study. The results demonstrate a significant enhancement in both thrust production and propulsive efficiency due to the stratification influence. Notably, the highest efficiency exceeding $80\,\%$ is achieved under moderate stratification conditions, surpassing the performance observed in a homogeneous fluid. We attribute this optimum performance to the proper match between the stratification effect and foil kinematics, which gives rise to intense vortex interactions and sufficient wave–mean flow interactions in the near wake of the oscillating foil. Consequently, the energy is transferred towards wake structures to form a high-intensity momentum jet in close proximity to the foil's trailing edge, indicating efficient propulsion. Furthermore, we find that the stratifications within the moderate-to-strong transitional regime display a reduced dependence of propulsive efficiency on the maximum angle of attack, primarily due to the delaying and alleviating effects on dynamic-stall events. Such a mechanism enables the oscillating foil to maintain a satisfactory performance by sufficiently high angles of attack without the penalty of stall events. Based on our findings, we propose that animals or artificial vehicles utilising oscillatory propulsion can benefit from the presence of density stratification in the surrounding fluid.

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics.

Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re, Strouhal St, and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k-ω-SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗, and its dependence on the Reynolds number, denoted as Re. This was performed following a power-law relationship of St∝Re(-α). We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St, Re, and Slip. Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.

CMBUV: A Composite-Mechanism Bioinspired Underwater Vehicle Integrated With Elasticity and Shear Damping Possesses High-Performance Capability

Benefiting from the potential advantages of low noise, high efficiency and little disturbance, bionic propulsion has attracted wide attentions. Compared with the rigid structure, the performance of the elastic propulsion structure such as flexible caudal fin and passive compliant joint has been improved, yet the effective frequency range is limited due to the single mechanism. The optimal propulsion can only be produced in a certain frequency range. In this article, a biological passive peduncle joint integrated with the composite mechanism of elasticity and shear damping is proposed, solving the problem of the narrow frequency range of effective propulsive capacity. Through the optimal regulation of the elastic function at a certain frequency range and characterization of the damping function which increases with frequency, the response features of the passive joint are optimized over a wide range of frequencies, thereby improving the propulsive performance of the composite-mechanism bioinspired underwater vehicle (CMBUV). A dynamic model is built and the deformation analysis of the compliant caudal fin is carried out. The propulsive efficiency is characterized, and the results indicate that the compliant caudal fin modulates the power transmission for enhancing thrust production. Extensive simulations and experiments reveal that the CMBUV achieves both high swimming speed with 4.42 body length per second and low cost of transport with 90.33 J kg <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-1}$</tex-math></inline-formula> m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-1}$</tex-math></inline-formula> . Bioinspired propulsion from this study takes advantage of undulating propulsion of natural fish, offering valuable insights into performing marine tasks in ocean environments.

Thermodynamic analysis of a high Mach number scramjet engine with secondary combustion for thrust enhancement

Intending to augment the thrust of air-breathing vehicles operating at high flight Mach numbers, especially under extreme flight conditions, this study introduced a pioneering methodology predicated on secondary combustion. This innovative scheme uses the product of combustion of hydrocarbon fuel and air to further react with metal fuel to obtain thrust gain. This study was mainly based on theoretical calculation. A preliminary parametric design and performance analysis of a Mach 8 scramjet engine with an afterburner was carried out based on the thermodynamic cycle analysis method, considering the gas component changes. The engine model design with an inward two-dimensional inlet was adopted, along with an oblique injection of hydrocarbon fuel and two combustors in series. In addition, the expansion of gas in a supersonic nozzle was modeled with quasi-one-dimensional flow equations. By maintaining an equivalence ratio of 1.0 for the hydrocarbon fuel in the primary combustor, meticulous exploration of the powder-to-gas ratio in the afterburner, ranging from 0.04 to 0.2, was conducted. Similarly, an investigation into the temperature ratio at the outlet of the inlet, spanning the range of 3.8 to 7, was performed. Through a judicious optimization process involving both the inlet compression temperature ratio and the magnesium powder's powder-to-gas ratio, the engine designed can obtain a maximum thrust gain of 57.3%. The analysis underscores the advantageous correlation between heightened powder-to-gas ratios and augmented thrust production. Setting the upper limit of the powder-gas ratio to 0.16 is recommended to maintain optimal performance. This research also provided a new idea for expanding the application of hydrocarbon fuels in higher flight Mach number scramjet engines.

In‐flight force estimation by flight mill calibration

AbstractThe study of insect flight is important for conservation and sustainability efforts, as predicting insect dispersal can aid management programmes in tackling economic and ecological harm from, for example, invasive species. Flight mills are invaluable tools for measuring the factors of insect flight under laboratory conditions, as they lower several technical and financial barriers to conduct experiments. It is especially difficult, however, to make assumptions about the energetic cost of tethered flights conducted using different tethers, or even on different flight mills, due to the mechanical variability of the bearing friction and air resistance of the rotating assembly. This additional uncertainty necessitates a larger number of replicates for any given standard of statistical confidence. By characterising flight mill friction, this uncertainty can both be reduced in magnitude and assigned a specific, well‐defined numerical value. We present a simple methodology to characterise this friction through dynamic calibration of the flight mill, at a high statistical confidence. This study uses videography of a flight mill undergoing free velocity decay due to friction, using an in‐house developed software to extract angular velocity from video data. However, the technique is readily adaptable to other measurement techniques. Using the velocity, alongside the mass moment of inertia of the flight mill, allows us to determine the rotational friction coefficient. This friction coefficient provides precise measurements of thrust production, and therefore the energy expenditure of flight, by the tethered insect.

New Insights into Sea Turtle Propulsion and Their Cost of Transport Point to a Potential New Generation of High-Efficient Underwater Drones for Ocean Exploration

Sea turtles gracefully navigate their marine environments by flapping their pectoral flippers in an elegant routine to produce the required hydrodynamic forces required for locomotion. The propulsion of sea turtles has been shown to occur for approximately 30% of the limb beat, with the remaining 70% employing a drag-reducing glide. However, it is unknown how the sea turtle manipulates the flow during the propulsive stage. Answering this research question is a complicated process, especially when conducting laboratory tests on endangered animals, and the animal may not even swim with its regular routine while in a captive state. In this work, we take advantage of our robotic sea turtle, internally known as Cornelia, to offer the first insights into the flow features during the sea turtle’s propulsion cycle consisting of the downstroke and the sweep stroke. Comparing the flow features to the animal’s swim speed, flipper angle of attack, power consumption, thrust and lift production, we hypothesise how each of the flow features influences the animal’s propulsive efforts and cost of transport (COT). Our findings show that the sea turtle can produce extremely low COT values that point to the effectiveness of the sea turtle propulsive technique. Based on our findings, we extract valuable data that can potentially lead to turtle-inspired elements for high-efficiency underwater drones for long-term underwater missions.

The hydrodynamic performance of duck feet for submerged swimming resembles oars rather than delta-wings

Waterfowl use webbed feet to swim underwater. It has been suggested that the triangular shape of the webbed foot functions as a lift-generating delta wing rather than a drag-generating oar. To test this idea, we studied the hydrodynamic characteristics of a diving duck’s (Aythya nyroca) foot. The foot’s time varying angles-of-attack (AoAs) during paddling were extracted from movies of ducks diving vertically in a water tank. Lift and drag coefficients of 3D-printed duck-foot models were measured as a function of AoA in a wind-tunnel; and the near-wake flow dynamics behind the foot model was characterized using particle image velocimetry (PIV) in a flume. Drag provided forward thrust during the first 80% of the power phase, whereas lift dominated thrust production at the end of the power stroke. In steady flow, the transfer of momentum from foot to water peaked at 45° < AoA < 60°, due to an organized wake flow pattern (vortex street), whereas at AoAs > 60° the flow behind the foot was fully separated, generating high drag levels. The flow characteristics do not constitute the vortex lift typical of delta wings. Rather, duck feet seem to be an adaptation for propulsion at a wide range of AoAs, on and below the water surface.

Transition phase in the static thrust generation of the biomimetic fin with low oscillating frequency

Biomimetic fin propulsion could be a promising solution for an efficient underwater propulsion mechanism. It could be designed to generate thrust for underwater locomotion efficiently. Many studies have proposed that the flexibility characteristics of the fin affect its effectiveness in thrust generation; for example, a flexible fin generates more thrust than a rigid fin. In this regard, the rigid fin may suffer a mechanical disadvantage in thrust generation. This study introduces the presence of thrust generation phases in biomimetic fins. The phases could be caused by the interaction of the fins and the surrounding fluid. To distinguish the phases clearly, the experimental setup in this study was designed for no-flow conditions. This study presents three phases of thrust generation: negative, transition, and positive. The existence of the negative and transition phases explains the mechanical disadvantages of the rigid fin. Within the range of evaluated fin frequencies, approximately 80% of the average net force of the rigid fin is in the negative and transition phases, compared to only 20% in flexible fins. In comparison to less flexible and rigid fins, a flexible fin could maximize positive thrust production three times higher at high frequency. The vector composition analysis and dye-injection flow visualization reveal the transition phase by emphasizing the balancing process between the surface friction of the fin and the inertial component of the force of the fluid and fin interaction. This study demonstrates the independence of the transition phase from the flexibility characteristics of the biomimetic fin. Because the bending characteristic of the flexible fin could direct more vectors in thrust generation, the fin could act as a thrust vectoring agent. The findings of this study could be used as a guide in designing and implementing high-performance fin propulsion in low-speed underwater locomotion.

Impact of jet velocity profile on the propulsive performance and vortex ring formation of pulsed jet propulsion

A squid-inspired jet propulsion system that indudes a deformable body and a nozzle exit attached to it is numerically studied. By prescribing the body deformation during a single discharge, we examine the impact of jet speed profiles on the vortex ring formation and propulsion performance of the system. Our results show that a secondary vortex ring following the leading vortex ring can be produced by the reverse cosine jet speed pattern at a given maximum stroke ratio, and for the other profiles (i.e., constant, cosine, reverse cosine, half cosine and rever half cosine styles) only distributed vortices are seen behind the leading vortex ring. The constant jet speed produces the largest time-averaged thrust due to jet momentum flux related thrust associated with its large jet speed. Except for the constant speed style, the largest mean thrust production and propulsion factor are obtained by the reverse cosine profile among the other four styles attributed to the formation of the secondary vortex ring. Nevertheless, this secondary vortex ring would not be produced at a small maximum stroke ratio for the reverse cosine speed fashion. We also find that the mean thrust production can reach a maximum under a specific maximum stroke ratio (Γm = 7.60) when two vortex rings are produced. This work may provide insight into the mechanical and control design of jet-based biomimetic propellers and robots.

A fundamental propulsive mechanism employed by swimmers and flyers throughout the animal kingdom.

Even casual observations of a crow in flight or a shark swimming demonstrate that animal propulsive structures bend in patterned sequences during movement. Detailed engineering studies using controlled models in combination with analysis of flows left in the wakes of moving animals or objects have largely confirmed that flexibility can confer speed and efficiency advantages. These studies have generally focused on the material properties of propulsive structures (propulsors). However, recent developments provide a different perspective on the operation of nature's flexible propulsors, which we consider in this Commentary. First, we discuss how comparative animal mechanics have demonstrated that natural propulsors constructed with very different material properties bend with remarkably similar kinematic patterns. This suggests that ordering principles beyond basic material properties govern natural propulsor bending. Second, we consider advances in hydrodynamic measurements demonstrating suction forces that dramatically enhance overall thrust produced by natural bending patterns. This is a previously unrecognized source of thrust production at bending surfaces that may dominate total thrust production. Together, these advances provide a new mechanistic perspective on bending by animal propulsors operating in fluids - either water or air. This shift in perspective offers new opportunities for understanding animal motion as well as new avenues for investigation into engineered designs of vehicles operating in fluids.

Fluid–structure resonance in spanwise-flexible flapping wings

We report direct numerical simulations of the flow around a spanwise-flexible wing in forward flight. The simulations were performed at$Re=1000$for wings of aspect ratio 2 and 4 undergoing a heaving and pitching motion at Strouhal number$St_c\approx 0.5$. We have varied the effective stiffness of the wing$\varPi _1$while keeping the effective inertia constant,$\varPi _0=0.1$. It has been found that there is an optimal aerodynamic performance of the wing linked to a damped resonance phenomenon, that occurs when the imposed frequency of oscillation approaches the first natural frequency of the structure in the fluid,$\omega _{n,f}/\omega \approx 1$. In that situation, the time-averaged thrust is maximum, increasing by factor 2 with respect to the rigid case with an increase in propulsive efficiency of approximately 15 %. This enhanced aerodynamic performance results from the combination of larger effective angles of attack of the outboard wing sections and a delayed development of the leading edge vortex. With increasing flexibility beyond the resonant frequency, the aerodynamic performance drops significantly, in terms of both thrust production and propulsive efficiency. The cause of this drop lies in the increasing phase lag between the deflection of the wing and the heaving/pitching motion, which results in weaker leading edge vortices, negative effective angles of attack in the outboard sections of the wing, and drag generation in the first half of the stroke. Our results also show that flexible wings with the same$\omega _{n,f}/\omega$but different aspect ratio have the same aerodynamic performance, emphasizing the importance of the structural properties of the wing for its aerodynamic performance.