Forward Propulsion Research Articles

Vibration Propulsion in Untethered Insect-Scale Robots with Piezoelectric Bimorphs and 3D-Printed Legs

This research presents the development and evaluation of a miniature autonomous robot inspired by insect locomotion, capable of bidirectional movement. The robot incorporates two piezoelectric bimorph resonators, 3D-printed legs, an electronic power circuit, and a battery-operated microcontroller. Each piezoelectric motor features ceramic plates measuring 15 × 1.5 × 0.6 mm3 and weighing 0.1 g, with an optimized electrode layout. The bimorphs vibrate at two flexural modes with resonant frequencies of approximately 70 and 100 kHz. The strategic placement of the 3D-printed legs converts out-of-plane motion into effective forward or backward propulsion, depending on the vibration mode. A differential drive configuration, using the two parallel piezoelectric motors and calibrated excitation signals from the microcontroller, allows for arbitrary path navigation. The fully assembled robot measures 29 × 17 × 18 mm3 and weighs 7.4 g. The robot was tested on a glass surface, reaching a maximum speed of 70 mm/s and a rotational speed of up to 190 deg./s, with power consumption of 50 mW, a cost of transport of 10, and an estimated continuous operation time of approximately 6.7 h. The robot successfully followed pre-programmed paths, demonstrating its precise control and agility in navigating complex environments, marking a significant advancement in insect-scale autonomous robotics.

Individual joint contributions to forward propulsion during treadmill walking in women with hip osteoarthritis.

As we age, reliance on the ankle musculature for push-off during walking reduces and increased reliance on the hip musculature is observed. It is unclear how joint pathology like osteoarthritis may affect this distal-to-proximal redistribution of propulsion. Here, we revisited a proof-of-concept study to study the effect of split-belt treadmill training, designed to reduce step length asymmetry, on forward propulsion during walking. Eleven women with hip osteoarthritis and five age-matched control participants walked on an instrumented split-belt treadmill at their preferred speed (hip osteoarthritis: 0.73 ± 0.11 m/s; controls: 0.59 ± 0.26 m/s). Women with hip osteoarthritis had less ankle power and propulsive force than controls, and greater hip contributions to forward propulsion on their involved limb. Following split-belt treadmill training, propulsive force increased on the involved limb. Five of 11 participants experienced a change in redistribution ratio that was greater than the minimal clinically meaningful difference. These "responders" had greater variability in pre-training redistribution ratio compared to non-responders. Women with hip osteoarthritis had poorer propulsive gait mechanics than controls yet split-belt treadmill training improved propulsive force. Redistribution ratio also changed in participants with high baseline variability. Our results suggest that split-belt treadmill training may be beneficial to people with hip osteoarthritis who have high variability in walking parameters. Further, the age-related shift to increased hip contributions to propulsion across populations of older adults may be due to increased variability during walking.

Experimental investigation on the hydrodynamic performance of a bioinspired manta-ray underwater vehicle in various forward propulsion modes

Bionic propulsion technology is revolutionizing underwater exploration by enabling underwater vehicles to navigate the oceans more efficiently. This research developed a scaled-down (10:1) experimental prototype of bionic manta-ray underwater vehicle, which has two degrees of freedom (2-DOF) pectoral fins: flapping and rotating. The impact of four different pectoral fin motion patterns (sinusoidal flapping and rotating, flapping frequency asymmetric, flapping amplitude offset, and rotating amplitude limitation) on the forward propulsion performance was investigated experimentally in a static water tunnel using a force/torque sensor and power analyzer. The results revealed that introducing asymmetry into the fin's flapping motion (asymmetric frequency or amplitude) significantly improved both average thrust and propulsive efficiency (the average thrust can be increased by more than 30%). Flapping with amplitude offset can effectively adjust its pitching moment without sacrificing much thrust. While the rotating motion of the pectoral fins contributes minimally to thrust generation compared to flapping, it plays an important role in enhancing both longitudinal stability and propulsive efficiency. Understanding the hydrodynamic performance of these various forward propulsion modes provides valuable insights for optimizing control strategies of bionic manta-ray underwater vehicles.

Kinematics-Based Predictions of External Loads during Handcycling.

The increased risk of cardiovascular disease in people with spinal cord injuries motivates work to identify exercise options that improve health outcomes without causing risk of musculoskeletal injury. Handcycling is an exercise mode that may be beneficial for wheelchair users, but further work is needed to establish appropriate guidelines and requires assessment of the external loads. The goal of this research was to predict the six-degree-of-freedom external loads during handcycling from data similar to those which can be measured from inertial measurement units (segment accelerations and velocities) using machine learning. Five neural network models and two ensemble models were compared against a statistical model. A temporal convolutional network (TCN) yielded the best predictions. Predictions of forces and moments in-plane with the crank were the most accurate (r = 0.95-0.97). The TCN model could predict external loads during activities of different intensities, making it viable for different exercise protocols. The ability to predict the loads associated with forward propulsion using wearable-type data enables the development of informed exercise guidelines.

Gait balance recovery after tripping: The influence of walking speed and ground inclination on muscle and joint function

Reactive lower limb muscle function during walking plays a key role in balance recovery following tripping, and ultimately fall prevention. The objective of this study was to evaluate muscle and joint function in the recovery limb during balance recovery after trip-based perturbations during walking. Twenty-four healthy participants underwent gait analysis while walking at slow, moderate and fast speeds over level, uphill and downhill inclines. Trip perturbations were performed randomly during stance, and lower limb kinematics, kinetics, and muscle contribution to the acceleration of the whole-body centre of mass (COM) were computed pre- and post-perturbation in the recovery limb. Ground slope and walking speed had a significant effect on lower limb joint angles, net joint moments and muscle contributions to support and propulsion during trip recovery (p < 0.05). Specifically, increasing walking speed during trip recovery significantly reduced hip extension in the recovery limb and increased knee flexion, particularly when walking uphill and at higher walking speeds (p < 0.05). Gluteus maximus played a critical role in providing support and forward propulsion of the body during trip recovery across all gait speeds and ground inclinations. This study provides a mechanistic link between muscle action, joint motion and COM acceleration during trip recovery, and underscores the potential of increased walking speed and ground inclination to increase fall risk, particularly in individuals prone to falling. The findings of this study may provide guidelines for targeted exercise therapy such as muscle strengthening for fall prevention.

Minimization of metabolic cost of transport predicts changes in gait mechanics over a range of ankle-foot orthosis stiffnesses in individuals with bilateral plantar flexor weakness

Neuromuscular disorders often lead to ankle plantar flexor muscle weakness, which impairs ankle push-off power and forward propulsion during gait. To improve walking speed and reduce metabolic cost of transport (mCoT), patients with plantar flexor weakness are provided dorsal-leaf spring ankle-foot orthoses (AFOs). It is widely believed that mCoT during gait depends on the AFO stiffness and an optimal AFO stiffness that minimizes mCoT exists. The biomechanics behind why and how an optimal stiffness exists and benefits individuals with plantar flexor weakness are not well understood. We hypothesized that the AFO would reduce the required support moment and, hence, metabolic cost contributions of the ankle plantar flexor and knee extensor muscles during stance, and reduce hip flexor metabolic cost to initiate swing. To test these hypotheses, we generated neuromusculoskeletal simulations to represent gait of an individual with bilateral plantar flexor weakness wearing an AFO with varying stiffness. Predictions were based on the objective of minimizing mCoT, loading rates at impact and head accelerations at each stiffness level, and the motor patterns were determined via dynamic optimization. The predictive gait simulation results were compared to experimental data from subjects with bilateral plantar flexor weakness walking with varying AFO stiffness. Our simulations demonstrated that reductions in mCoT with increasing stiffness were attributed to reductions in quadriceps metabolic cost during midstance. Increases in mCoT above optimum stiffness were attributed to the increasing metabolic cost of both hip flexor and hamstrings muscles. The insights gained from our predictive gait simulations could inform clinicians on the prescription of personalized AFOs. With further model individualization, simulations based on mCoT minimization may sufficiently predict adaptations to an AFO in individuals with plantar flexor weakness.

“Something comes through or it doesn’t”: intensive reading in post-qualitative inquiry

The article describes practices of “intensive reading” for post-qualitative inquiry, drawing on the work of Deleuze, with some examples from the author’s own research. To read intensively is to experience the forward propulsion toward something not-yet-present. That forward momentum, and the fragmented path that it carves through the library, has the potential, in the words of Stengers, to summon something “that has no stable illustration in this world.”

Société de Biomécanique young investigator award 2022: Effects of applying functional electrical stimulation to ankle plantarflexor muscles on forward propulsion during walking in young healthy adults

The triceps surae muscle, composed of the gastrocnemius and soleus muscles, plays a major role in forward propulsion during walking. By generating positive ankle power during the push-off phase, these muscles produce the propulsive force required for forward progression. This study aimed to test the hypothesis that applying functional electrical stimulation (FES) to these muscles (soleus, gastrocnemius or the combination of the two) during the push-off phase would increase the ankle power generation and, consequently, enhance forward propulsion during walking in able-bodied adults. Fifteen young adults walked at their self-selected speed under four conditions: no stimulation, with bilateral stimulation of the soleus, gastrocnemius, and both muscles simultaneously. Muscles were stimulated just below the discomfort threshold during push-off, i.e., from heel-off to toe-off. FES significantly increased ankle power (+22 to 28 % depending on conditions), propulsive force (+15 to 18 %) and forward progression parameters such as walking speed (+14 to 20 %). Furthermore, walking speed was significantly higher (+5%) for combined soleus and gastrocnemius stimulation compared with gastrocnemius stimulation alone, with no further effect on other gait parameters. In conclusion, our results demonstrate that applying FES to the gastrocnemius and soleus, separately or simultaneously during the push-off phase, enhanced ankle power generation and, consequently, forward propulsion during walking in able-bodied adults. Combined stimulation of the soleus and gastrocnemius provided the greatest walking speed enhancement, without affecting other propulsion parameters. These findings could be useful for designing FES-based solutions for improving gait in healthy people with propulsion impairment, such as the elderly.

Hydrodynamic analysis of the upright swimming of seahorse

The seahorse is the only creature in the ocean that can maintain an upright posture while swimming. This paper mainly discusses the hydrodynamic characteristics and the flow field structure of the seahorse when it swims upright. Using a three-dimensional seahorse model, numerical simulations of self-propelled swimming are conducted by establishing the kinematic equations of its dorsal fin. The focus is on elucidating the effects of the undulation frequency and the inclination angle on swimming performance. The results indicate that a higher undulation frequency of the dorsal fin leads to better acceleration performance, or in other words, greater hydrodynamic forces. The inclination angle of the seahorse's body also directly affects its hydrodynamics and the flow field structure. Unlike other fish that swim horizontally, the seahorse generates forward and upward thrust as the flow field simultaneously spreads backward and downward. Since the upright posture makes the forward thrust much smaller than the upward one, the seahorse has low efficiency in forward propulsion when swimming upright. As the inclination angle decreases, the forward thrust gradually increases and exceeds the upward force, which allows for a rapid improvement in the swimming velocity. The simulation findings of this study are consistent with previous experimental observations.

Bioinspired Design and Experimental Validation of an Aquatic Snake Robot.

This article presents the design, simulation, and experimental validation of a novel modular aquatic snake robot capable of surface locomotion. The modular structure allows each unit to function independently, facilitating ease of maintenance and adaptability to diverse aquatic environments. Employing the material point method with the moving least squares (MPM-MLS) simulation technique, the robot's dynamic behavior was analyzed, yielding reliable results. The control algorithm, integral to the robot's autonomous navigation, was implemented to enable forward propulsion at high speed, steering, and obstacle detection and avoidance. Extensive testing of the aquatic snake robot was conducted, demonstrating its practical viability. The robot showcased promising swimming capabilities, achieving high speeds and maneuverability. Furthermore, the obstacle detection and avoidance mechanisms were proven effective, showing the robot's ability to navigate through dynamic environments. The presented aquatic snake robot represents an advancement in the field of underwater robotics, offering a modular and versatile solution for tasks ranging from environmental monitoring to search and rescue operations.

Assessment of Foot Strike Angle and Forward Propulsion with Wearable Sensors in People with Stroke.

Effective retraining of foot elevation and forward propulsion is a critical aspect of gait rehabilitation therapy after stroke, but valuable feedback to enhance these functions is often absent during home-based training. To enable feedback at home, this study assesses the validity of an inertial measurement unit (IMU) to measure the foot strike angle (FSA), and explores eight different kinematic parameters as potential indicators for forward propulsion. Twelve people with stroke performed walking trials while equipped with five IMUs and markers for optical motion analysis (the gold standard). The validity of the IMU-based FSA was assessed via Bland-Altman analysis, ICC, and the repeatability coefficient. Eight different kinematic parameters were compared to the forward propulsion via Pearson correlation. Analyses were performed on a stride-by-stride level and within-subject level. On a stride-by-stride level, the mean difference between the IMU-based FSA and OMCS-based FSA was 1.4 (95% confidence: -3.0; 5.9) degrees, with ICC = 0.97, and a repeatability coefficient of 5.3 degrees. The mean difference for the within-subject analysis was 1.5 (95% confidence: -1.0; 3.9) degrees, with a mean repeatability coefficient of 3.1 (SD: 2.0) degrees. Pearson's r value for all the studied parameters with forward propulsion were below 0.75 for the within-subject analysis, while on a stride-by-stride level the foot angle upon terminal contact and maximum foot angular velocity could be indicative for the peak forward propulsion. In conclusion, the FSA can accurately be assessed with an IMU on the foot in people with stroke during regular walking. However, no suitable kinematic indicator for forward propulsion was identified based on foot and shank movement that could be used for feedback in people with stroke.

Reinventing the wheel for a manual wheelchair

Purpose Standard manual wheelchairs (MWCs) are inefficient and pushrim propulsion may cause progressive damage and pain to the user’s arms. We describe a wheel for a MWC with a novel propulsion mechanism. Methods The wheel has two modes of operation called “Standard” mode and “Run” mode. In Run mode, the wheelchair is propelled forward by pushing a compliant handle forward and then pulling it back, both strokes contributing to forward propulsion. We report the propulsive force and preliminary testing on a rough outdoor circuit by three able-bodied participants. Results In Run mode, the peak applied force is reduced to 30% and the maximum force gradient is reduced to 10% of that for standard pushrim propulsion, for the same work output. The travel time for the 1.06 km outdoor circuit is about 60% of that for a brisk walk and about 40% of that for pushrim propulsion. At a propulsion speed of 1 m/s, the cardiovascular effort in Run mode is 56% of that for pushrim propulsion. Automatic hill-hold in Run mode improves safety when ascending slopes. The mechanism has three gears so that it can be used by people with widely varying strength and fitness. Folding the handle away converts the operation to Standard mode with the conventional pushrim propulsion, supplemented by three gears. Conclusions Despite the increased weight, width and friction, the bimodal geared wheels facilitate wheelchair travel on challenging paths. This may bring significant improvement to the quality of life of MWC users.

A self-propelling clapping body

We report an experimental study of the motion of a clapping body consisting of two flat plates pivoted at the leading edge by a torsion spring. Clapping motion and forward propulsion of the body are initiated by the sudden release of the plates, initially held apart at an angle $2\theta _o$ . Results are presented for the clapping and forward motions, and for the wake flow field for 24 cases, where depth-to-length ratio ( $d^* = 1.5,1\text { and }0.5$ ), spring stiffness per unit depth ( $Kt$ ), body mass ( $m_b$ ) and initial separation angle ( $2\theta _o = 45^{\circ }\text { and }60^{\circ }$ ) are varied. The body initially accelerates rapidly forward, then slowly retards to nearly zero velocity. Whereas the acceleration phase involves a complex interaction between plate and fluid motions, the retardation phase is simply fluid dynamic drag slowing the body. The wake consists of either a single axis-switching elliptical vortex loop (for $d^* = 1\text { and }1.5$ ) or multiple vortex loops (for $d^* = 0.5$ ). The body motion is nearly independent of $d^*$ and most affected by variation in $\theta _o$ and $Kt$ . Using conservation of linear momentum and conversion of spring strain energy into kinetic energy in the fluid and body, we obtain a relation for the translation velocity of the body in terms of the various parameters. Approximately 80 % of the initial stored energy is transferred to the fluid, only 20 % to the body. The experimentally obtained cost of transport lies between 2 and $8\ \mathrm {J}\ \mathrm {kg}^{-1}\ \mathrm {m}^{-1}$ .

Design and Evaluation of Hybrid Passive Spring Damper Ankle Foot Orthosis for Gait Performance in Drop Foot Patients: A Feasibility Study.

Passive and hybrid passive Ankle foot orthoses (AFOs) are the prevalent prescription in drop foot patients to prevent toe dragging during the swing phase. While, these AFOs have some limitations like inability to overcome foot slap, limitation in forward propulsion and inappropriate power generate at the push off. The aim of this study was to design a novel spring damper and evaluate the immediate effects of this AFO on improving the ankle kinetic and kinematic in drop foot patients. This AFO was generated from carbon composite frame and foot section with posterior hinge and spring damper actuator that controlled plantar flexion resistance at the early stance, freely dorsi flexion movement with the ability to store energy during mid-stance movement as well as restore this energy at the pre swing phase. This AFO was assessed on ten drop foot patients who used Posterior Leaf Spring AFO conditions and walked at their self-comfortable walking speed. Then the ankle kinetic and kinematic data in two conditions of with PLS (Posterior Leaf Spring) AFO, and novel spring damper AFO were assessed. Results showed a significant improve in the immediate effect of the kinetic and kinematic parameters. In conclusion, spring damper AFO improved all ankle angles in entire gait cycle as well as the ankle moments and power. Therefore, this AFO should be consider as a selective AFO in drop foot patients.

Hydrodynamic Performance of Soft Robotic Fish Actuated by Ionic Polymer-Metal Composite Pectoral Caudal Fin

Soft robotic fish has a lot of benefits. This paper aims to create a robotic fish with a soft pectoral caudal fin which was powered by IPMC material. The soft robotic fish’s hydrodynamic performance during straight swimming is numerically computed using the overset grid approach. Compared with the soft tail fin driven with a driving frequency of 0.05 Hz and those driven together with three soft pectoral fins with different driving frequencies and amplitude, the hydrodynamic coefficients and pressure of the bionic robotic fish are analyzed. We can find the regions of distinct positive and negative pressure during the IPMC soft caudal fin flapping. And the forward pressure component provides forward propulsion for the bionic fish. The greater the flapping frequency of the IPMC soft pectoral fin is, the smaller the amplitude is, and the greater the drag force receives. It is concluded that while the driving frequency of soft pectoral fins is 0.05 Hz, the amplitude is 5.64 mm, and the soft pectoral fin driving effect is good. Further research into how soft pectoral caudal fin frequency and amplitude affect the hydrodynamic capabilities of bionic fish was also made.

Thrust generation and propulsive efficiency in dolphin-like swimming propulsion

Given growing interest in emulating dolphin morphology and kinematics to design high-performance underwater vehicles, the current research effort is dedicated to studying the hydrodynamics of dolphin-like oscillatory kinematics in forward propulsion. A computational fluid dynamics method is used. A realistic three-dimentional surface model of a dolphin is made with swimming kinematics reconstructed from video recording. The oscillation of the dolphin is found to enhance the attachment of the boundary layer to the posterior body, which then leads to body drag reduction. The flapping motion of the flukes is found to generate high thrust forces in both the downstroke and the upstroke, during which vortex rings are shed to produce strong thrust jets. The downstroke jets are found to be on average stronger than the upstroke jet, which then leads to net positive lift production. The flexion of the peduncle and flukes is found to be a crucial feature of dolphin-like swimming kinematics. Dolphin-inspired swimming kinematics were created by varying the flexion angle of the peduncle and flukes, which then resulted in significant performance variation. The thrust benefits and propulsive efficiency benefits are associated with a slight decrease and slight increase of the flexion of the peduncle and flukes, respectively.

EFFECTS OF A NORDIC WALKING INTERVENTION ON WALKING IN NORMAL ADULTS

The purpose of this study was to compare and examine gait parameters, hip joint angle, and lower extremity muscle activity during normal walking before and after Nordic walking (NW) intervention. Nineteen healthy male participants (age 26.3 ± 2.4 years) were included in the study. During walking, we measured gait parameters using the footprint-measuring gait analysis system. Аngular changes of the hip joint were measured with an IMU-type portable three-dimensional motion analyzer and the EMG activity of each muscle. The measurements above were performed before and after a one-hour NW training course. The hip joint angle, muscle activity, and gait parameters were compared before and after the intervention with the same participants. In gait parameters, the stride length and walking speed were significantly greater after the intervention, while the cadence decreased significantly. Both hip flexion and extension angles were significantly greater after the intervention. In terms of muscle activity, the rectus abdominis, the tibialis anterior, and the gastrocnemius were very different after the intervention. According to previous reports, employing a large stride length during NW would affect the normal gait after the training. The use of the Nordic pole may have stimulated a substantial forward movement in the lower extremities using the large range of motion of the hip joints. The benefits of NW include enhanced forward propulsion during gait and additional stability during the stance phase due to the greater support surface provided by the poles.

The influence of backward versus forward locomotor training on gait speed and balance control post-stroke: Recovery or compensation?

Backward walking training has been reported to improve gait speed and balance post-stroke. However, it is not known if gains are achieved through recovery of the paretic limb or compensations from the nonparetic limb. The purpose of this study was to compare the influence of backward locomotor training (BLT) versus forward locomotor training (FLT) on gait speed and dynamic balance control, and to quantify the underlying mechanisms used to achieve any gains. Eighteen participants post chronic stroke were randomly assigned to receive 18 sessions of either FLT (n = 8) or BLT (n = 10). Pre- and post-intervention outcomes included gait speed (10-meter Walk Test) and forward propulsion (time integral of anterior-posterior ground-reaction-forces during late stance for each limb). Dynamic balance control was assessed using clinical (Functional Gait Assessment) and biomechanical (peak-to-peak range of whole-body angular-momentum in the frontal plane) measures. Balance confidence was assessed using the Activities-Specific Balance Confidence scale. While gait speed and balance confidence improved significantly within the BLT group, these improvements were associated with an increased nonparetic limb propulsion generation, suggesting use of compensatory mechanisms. Although there were no improvements in gait speed within the FLT group, paretic limb propulsion generation significantly improved post-FLT, suggesting recovery of the paretic limb. Neither training group improved in dynamic balance control, implying the need of balance specific training along with locomotor training to improve balance control post-stroke. Despite the within-group differences, there were no significant differences between the FLT and BLT groups in the achieved gains in any of the outcomes.

“Posture first”: Interaction between posture and locomotion in people with low back pain during unexpectedly cued modification of gait initiation motor command

The ability to adapt anticipatory postural adjustments (APAs) in response to perturbations during single-joint movements is altered in people with chronic low back pain (LBP), but a comprehensive analysis during functional motor tasks is still missing. This study aimed to compare APAs and stepping characteristics during gait initiation between people with LBP and healthy controls, both in normal (without cue occurrence) condition and when an unexpected visual cue required to switch the stepping limb. Fourteen individuals with LPB and 10 healthy controls performed gait initiation in normal and switch conditions. The postural responses were evaluated through the analysis of center of pressure, propulsive ground reaction forces, trunk and whole-body kinematics, and activation onsets of leg and back muscles. During normal gait initiation, participants with LBP exhibited similar APAs and stepping characteristics to healthy controls. In the switch condition, individuals with LBP were characterized by greater mediolateral postural stability but decreased forward body motion and propulsion before stepping. The thorax motion was associated with forward propulsion parameters in both task conditions in people with LBP but not healthy controls. No between-group differences were found in muscle activation onsets. The results suggest that postural stability is prioritized over forward locomotion in individuals with LBP. Furthermore, the condition-invariant coupling between thorax and whole-body forward propulsion in LBP suggests an adaptation in the functional use of the thorax within the postural strategy, even in poor balance conditions.

A Simplified Mathematical Model of Pumped Hydrofoils

This paper presents a simplified mathematical model of a pumped hydrofoil (PH)—a surfboard elevated above water surface and connected to a tandem of hydrofoils by a strut. The PH is operated by a rider who stands on the surfboard and produces swinging up-and-down motions resulting in forward propulsion of the device. In the present paper, the description of the vertical motion of the PH is reduced to a linear oscillator excited by an oscillating mass coupled with the requirement that the weight is supported by dynamic lift of the foil(s). The inertial and damping influence of the hydrofoil(s) is accounted for by expanding unsteady lift force on the foil(s) in terms of kinematic parameters. The restoring term of the oscillator is associated with the phenomenon of automatic stabilization of shallowly submerged hydrofoils. The latter effect manifests itself in that when a hydrofoil approaches free surface, its lift decreases, and when it moves away from free surface, its lift increases. The analytical solution of the pumping foil mass-spring type forced oscillations equation allows one to calculate the flapping motion of the foil(s) and, thereafter, the period-averaged thrust generated by the PH. The resulting speed has been estimated on an assumption that the device enters its cruising mode when the thrust becomes equal to the drag, the latter comprising viscous, wave, and induced drag components. The model under discussion allows one to relate the main parameters of the system to its performance and, hopefully, provides further insight into the pumped hydrofoil phenomenon, its design methodology, and operation strategy. The review part of the paper focuses on two aspects of the problem: hydrodynamic behavior of the hydrofoil(s) in proximity to free water surface and their propulsion due to oscillations.