Mean Aerodynamic Forces Research Articles

Experimental study on aerodynamic countermeasure for galloping vibration of stay cables attached with lamps: Perforated shrouds

The aerodynamic countermeasure of the perforated shrouds is proposed to reduce the galloping vibration of stay cables installed with rectangular lamps. Ten test models with different parameters were designed and manufactured and a series of wind tunnel tests were carried out to measure the aerodynamic forces on the test models. Then, the mean aerodynamic force coefficients were obtained to further calculate the galloping force coefficients of these test models. Based on the quasi-steady theory, the effectiveness of the perforated shrouds on mitigating galloping vibration was verified by considering the effects of porosities, hole types, shroud diameter, the turbulence of approaching flow, and cable orientation (vertical and inclined). The cable inclination of 35° and a turbulence intensity of 9% was used for the force measurement wind tunnel tests, as well as shrouds with porosities of 0, 8.7%, 19.6%, 28.3%, 34.9%, 36%, 44.2%, and 49.0%. Two types of holes, including circular staggered and square array holes, were adopted, and two outer diameters of the perforated shrouds (125 mm and 88 mm) were used. The results show that the perforated shroud with a diameter of 125 mm plays an important role in mitigating the galloping vibration of both vertical and inclined stay cables with rectangular lamps. For the vertical test model, it seems that the optimal porosity of the perforated shroud is 19.6%, and the optimal porosity of the perforated shrouds for the inclined test model is within the range of 19.6%–34.9%. The minimum galloping force coefficients Cg of them is all greater than 0. The galloping critical wind velocity of the inclined cable-lamp structure without perforated shrouds is significantly lower than that of the vertical cable. However, the inclination of the stay cable induces a higher galloping critical wind velocity if the perforated shrouds are installed. The type of holes, a circular staggered and rectangular array, seems to not affect the galloping vibration. The turbulence intensity of 9% has a significant effect on the galloping critical wind velocity for the vertical and inclined cable attached with rectangular lamps without perforated shrouds but has little effect on the galloping critical wind velocity of the vertical and inclined cable-lamp system with perforated shrouds. The maximum value of combined aerodynamic mean force coefficients CC for the vertical test model with the perforated shroud is the same (1.1), the maximum wind load of the inclined test model with the perforated shroud is increased by 21∼58% due to the larger diameter.

Effects of twisted wind flow on the mean wind load characteristics of super high-rise buildings with different heights

The phenomena of wind veering are frequently observed in the atmospheric boundary layer, and their influences have gradually attracted attention in the evaluation of wind effects of super high-rise buildings. However, most studies only focus on buildings with a certain height, and the wind load characteristics of buildings with different heights under twisted wind flows (TWFs) are not clear. This paper investigates the wind veering effects on mean wind load characteristics of square cross-sectional super high-rise buildings with different heights (1000 m, 800 m, 600 m) via wind tunnel test under TWFs. The mean wind pressure and aerodynamic force characteristics of three models under TWFs with different wind twist angles are analyzed, and the effects of wind twist angles on the aerodynamic forces and deviation phenomenon (including amplitude shift and angle shift) are discussed in detail. Finally, the effects of wind twist angle on amplitude and angle shifts in the longitudinal, lateral, and torsional directions are quantified, and the unfavorable layers are assessed. The results show that the effect of wind veering on the mean aerodynamic characteristics does not change monotonously with the wind twist angle, and the mean aerodynamic characteristics of models with different heights can be equivalent to wind twist angles at the top of building. When the wind twist angle is smaller than 6.2°, the wind veering effect can be ignored. The objective of this study is to explore the wind loads characteristics of super high-rise buildings with different heights under TWFs, furthermore, to provide useful information for further investigation and future wind-resistant design of skyscrapers.

Correlations between flexural stiffness, wingbeat frequency and aerodynamic force generation in hovering insect flight

We report a direct relationship between wing flexural stiffness, wingbeat frequency, and mean aerodynamic force generation based on the wing morphological database for various insect species in hovering flight condition. Proposed correlations have shown the potential to predict the minimum aerodynamic force generation in flapping wings for a given flapping frequency with reasonable accuracy. The robustness of these correlations is demonstrated by validating them against the available experimental data for the various artificial flapping-wing configurations. These regression models can be used as first-order design tools which will save computational and experimental time while developing flapping-wing drones.

Effect of ice accretion on aerodynamic characteristics of pipeline suspension bridges

Pipeline suspension bridges may confront the issue of ice accretion in areas prone to glaze ice or rime. Ice accretion is known to influence the wind-induced responses of various structures, while the effects on the wind-induced responses of pipeline suspension bridges received little attention. To this end, this paper investigated the effect of ice accretion on the aerodynamic characteristics of pipeline suspension bridges from a series of wind tunnel tests. The influences of the shape of cross-section, ice shape, ice class, and Reynolds number on mean aerodynamic force coefficients were examined through static wind tunnel tests. The galloping stability was further examined based on the quasi-steady galloping theory according to the mean aerodynamic force coefficients. Furthermore, the effects of ice class and ice shape on the aeroelastic stability and flutter derivatives of a pipeline suspension bridge were investigated through dynamic wind tunnel tests. The results comprehensively reveal how ice accretion affects the aerodynamic characteristics of the bridge. Ice accretion on the girder can increase the static aerodynamic force, probability of galloping, and leads to vortex-induced vibration. Research results can provide a basis for aerostatic and buffeting analyses and a reference for the wind-resistant design of similar bridges in cold regions.

Mean wake and aerodynamic forces for surface-mounted finite-height square prisms of very small aspect ratio

The mean flow field, aerodynamic forces, bending moment and Strouhal number (St) were investigated for isolated surface-mounted finite-height square prisms of very small aspect ratio (AR). The Reynolds number was Re =7.5×104 for the velocity measurements and 9×104 for the force, bending moment and St measurements. Prisms with AR = 0.5, 0.7 and 1 were considered, under two different boundary layer thicknesses of δ/D=0.7–0.8 (thin) and δ/D=1.3 (thick). For both boundary layers, the mean drag force coefficient showed a sharper increase with AR compared with taller prisms, and the mean normal force coefficient increased smoothly, with a lower magnitude than pressure-based normal force coefficients. An approximately constant point of action of the drag force was found for AR < 1. While the thick boundary layer caused the spectral peaks to weaken and St to decrease, some periodicity was still found for all AR. These features were connected to the changes in the mean wake of the prisms with AR and δ/D. A smaller AR and larger δ/D had similar effects, causing the wake to shorten, the probability and type of reattachment of the flow on the free end to change, and the mean wake structure to transition from a streamwise wake vorticity pattern to an inner vorticity pattern. The prism with AR = 1 showed a dipole wake structure similar to that of taller prisms, while the unique wake topology of prisms with AR < 1 was found to be responsible for the different force and St trends identified in this range of AR.

Wind turbine response in waked inflow: A modelling benchmark against full-scale measurements

Predicting the power and loads of wind turbines in waked inflow conditions still presents a major modelling challenge. It requires the accurate modelling of the atmospheric flow conditions, wakes of upstream turbines and the response of the turbine of interest. Rigorous validations of model frameworks against measurements of utility-scale wind turbines in such scenarios remain limited to date. In this study, six models of different fidelity are compared against measurements from the DanAero experiment. The two benchmark cases feature a full-wake and partial-wake scenario, respectively. The simulations are compared against local pressure forces and inflow velocities measured on several blade sections of the downstream turbine, as well as met mast measurements and standard SCADA data. Regardless of the model fidelity, reasonable agreements are found in terms of the wake characteristics and turbine response. For instance, the azimuth variation of the mean aerodynamic forces acting on the blade was captured with a mean relative error of 15–20%. While various model-specific deficiencies could be identified, the study highlights the need for further full-scale measurement campaigns with even more extensive instrumentation. Furthermore, it is concluded that validations should not be limited to integrated and/or time-averaged quantities that conceal characteristic spatial or temporal variations.

A two-way coupling method for the study of aeroelastic effects in large wind turbines

The relevant size of state-of-the-art wind turbines suggests a significant Fluid-Structure Interaction. Given the difficulties to measure the phenomena occurring, researchers advocate high-fidelity numerical models exploiting Computational Fluid and Structural Dynamics. This work presents a novel aeroelastic model for wind turbines combining our Large-Eddy Simulation fluid solver with a modal beam-like structural solver. A loose algorithm couples the Actuator Line Model, which represents the blades in the fluid domain, with the structural model, which represents the flexural and torsional deformations. For the NREL 5 MW wind turbine, we compare the results of three sets of simulations. Firstly, we consider one-way coupled simulations where only the fluid solver provides the structural one with the aerodynamic loads; then, we consider two-way coupled simulations where the structural feedback to the fluid solver is made of the bending deformation velocities only; finally, we add to the feedback the torsional deformation. The comparison suggests that one-way coupled simulations tend to overpredict the power production and the structural oscillations. The flapwise blades vibration induces a significant aerodynamic damping in the structural motion, while the nose-down torsion reduces the mean aerodynamic forces, and hence the power, yet without introducing a marked dynamical effect.

The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Girder

To investigate the aerodynamic characteristics of a twin-box girder in turbulent incoming flow, we carried out wind tunnel tests, including two aerodynamic interferences: leading body-height grid, and leading circular cylinder. In this study, the pressure distribution and the mean and fluctuating aerodynamic forces with the two interferences are compared with bare deck in detail to investigate the relationship between aerodynamic characteristics and the incoming flow characteristics (including Reynolds number and turbulence intensity). The experimental results reveal that, owing to the body-height flow characteristics around the deck interfered with by the body-height grid, the disturbed aerodynamic characteristics of the twin-box girder differ considerably from those of the bare twin-box girder. At the upstream girder, due to the vortex emerging from the body-height grid breaking the separation bubble, pressure plateaus in the upper and lower surface are eliminated. In addition, the turbulence generated by the body-height grid reduces the Reynolds number sensitivity of the twin-box girder. At a relatively high Reynolds number, the fluctuating forces are mainly dominated by turbulence intensity, and the time-averaged forces show almost no change under high turbulence intensity. At a low Reynolds number, the time-averaged forces change significantly with the turbulence intensity. Moreover, at a low Reynolds number, the wake of the leading cylinder effectively forces the boundary layer to transition to turbulence, which reduces the Reynolds number sensitivity of the mean aerodynamic forces and breaks the separation bubbles. Additionally, the fluctuating drag force and the fluctuating lift force are insensitive to the diameter and the spacing ratio.

Effect of cable surface geometry and ice accretion shapes on the aerodynamic behaviour of inclined stay cables

A wind-tunnel study has been conducted to evaluate changes in the aerodynamic behaviour of stay cables of a bridge due to ice accretion from freezing rain and, due to different cable surface geometries. Numerical simulations were performed to predict the three-dimensional ice shapes resulting from freezing rain for a variation of environmental conditions: wind speed, wind direction, air temperature, velocity of precipitation and duration of precipitation. Stay-cable models were fabricated using laser selective sintering for three different surface geometries (double helical fillet, concentric rings, and double helical strakes) with ice formed under the same environmental conditions. Additional models with the helical fillet geometry were fabricated to evaluate the effect of the air temperature at which ice was formed, the effect of wind direction during the precipitation event and the effect of the duration of the precipitation. The aerodynamic drag and lift forces acting on the models were measured for different wind speeds and cable-wind angles. The overall study evaluated the mean aerodynamic force coefficients of ten models in smooth flow, and two of the models were also tested in turbulent flow. The critical Reynolds number regime for the models of stay cable with ice accretion shapes occurred at a lower Reynolds number (below 100,000) than for the un-iced cables and the drag coefficient was less sensitive to increases in Reynolds numbers than the equivalent un-iced cables. These effects were attributed to the combined role of the ice-shape in determining the separation point combined with the higher surface roughness of the ice. An important observation was that for the three surface geometries and the range of test conditions that were considered, the maximum drag coefficients for ice-accreted models ranged from approximately 1.1 to 1.3, and were up to 50% greater than those observed without ice. The model with helical strakes and ice accretion exhibited the highest drag coefficient and exhibited more variation in lift coefficient with changes in Reynolds number than the other two cable surface geometries. The aerodynamic forces of an ice-accreted model followed similar trends in smooth and turbulent flow, but the drag coefficients were greater in turbulent flow. The presence and shape of the ice appeared to have a more dominant effect on the separation behaviour of the models than the presence of turbulence (for an ice-accreted model). The aerodynamic coefficients did not change greatly between the cases where ice was accreted at −0.5°C and −1.5°C due to the similar ice shape and thickness near the separation locations. The ice shape formed at −5°C was thicker but more localized and resulted in drag and lift coefficients that had greater variation with changes in the cable-wind plane. The effect of ice duration from 10 h to 20 h resulted in a increased variation in mean lift coefficient behaviour due to the asymmetric shape that resulted from the ice accretion parameters.

Vortex flow aerodynamics behind a symmetric airfoil at low angles of attack and Reynolds numbers

The low Reynolds number aerodynamics is important to investigate for micro air vehicle applications. The current paper covers numerical simulations to present the downstream development of the wake patterns and detailed analysis of the vortices generated at the downstream of NACA 0012 airfoil around the critical angle of attack where the instantaneous vortex patterns are oscillatory and differ from the mean vortex pattern for low Reynolds numbers ranging from 1000 to 4000. The instantaneous and mean aerodynamic forces, pressure and skin friction coefficients, and vorticity values are compared in addition to the path of the vortex centers, their longitudinal and lateral spacings, Kármán spacing ratios, and distortion ratios at the wake of the airfoil in regard to the different Reynolds numbers investigated. The streamwise and crosswise velocities of the vortex cores and relative velocities at different transverse locations are also discussed and presented in detail. The correlations between different non-dimensional numbers (St, Re, Ro) are obtained at these low Reynolds numbers investigated.

Experimental study on aerodynamic characteristics of a large-diameter ice-accreted cylinder without icicles

The aerodynamic characteristics of a circular cylinder (diameter ​= ​600 ​mm) with and without ice accretion (without icicles) were studied via wind tunnel tests (including simultaneous multi-pressure and force measurements) for Reynolds numbers (Re) of 1.29 ​× ​105–1.27 ​× ​106. The influences of wind angle of attack α, turbulence intensity Iu, relative surface roughness k, and accreted ice shape on the mean aerodynamic force coefficients (MAFCs), mean pressure coefficients, and pressure correlation coefficients were comprehensively investigated. Experimental results showed that the MAFCs of the ice-accreted cylinders exhibited significant Reynolds number effects, and the effects were closely related to the ice shape. The effects of Iu and k on the drag force of the ice-accreted and ice-free cylinders were similar. The remarkable lift force due to the asymmetric ice accretion could be reduced by increasing k and Iu. The effect of α on the MAFCs was related to the ice shapes and Re. The flow reattachments in the critical and supercritical regimes were examined to reveal the flow states around the finite ice-free and ice-accreted cylinders. The flow-fields around the finite ice-free and ice-accreted cylinders had significant three-dimensional effects, which could be weakened by introducing the Iu and k. The findings of this study could provide further understanding of the effect of ice accretion on the aerodynamic characteristics of circular cylinders. The results could be used as beneficial references in the wind-resistance design of ice-accreted circular cylinders.

Large eddy simulation of dynamic stall flow control for wind turbine airfoil using plasma actuator

To solve aerodynamic performance deterioration caused by dynamic stall, a large eddy simulation numerical calculation based on dynamic grid and sliding grid technology was conducted and the dynamic flow control mechanism of unsteady pulsed plasma was explored. The results showed that plasma aerodynamic actuators can effectively control the airfoil’s dynamic stall, improve the mean and transient aerodynamic forces, and reduce the negative peak value of the pitch moment and hysteresis loop area. A negative pressure “bulge” appears in the plasma application areas, and the peak suction of the airfoil’s upper surface obviously increases. Two unsteady control parameters, the pulsed frequency and duty cycle, significantly influence the flow control. When the dimensionless pulsed frequency is 1.5, plasma control improves, and when the duty cycle is 0.8, it is close to the aerodynamic benefits under the continuous working mode. In the deep stall state, plasma impels the flow separation position to obviously move backward, resisting large-scale dynamic stall vortices. The structure of the separation vortices is broken, dissipated, and reattached to the airfoil by the plasma, and the influence area of the vortices is reduced. In the light stall state, the plasma actuator easily controls the shear layer, inducing the transition of the airfoil’s boundary layer and promoting the momentum mixing with the main flow. “Vortex clusters” near the airfoil’s leading edge induced by plasma actuation play a role in the virtual aerodynamic shape. The harmonic oscillation of aerodynamic force/moment is caused by the nonlinear and strong coupling effect between dynamic vortex structures with different scales and frequencies and plasma aerodynamic actuation. The amplitude of low-order mode energy concentration is relatively large, which is mainly caused by the pitching motion. The high-order fluctuation energy concentration is caused by the evolution process of starting vortices and derived secondary vortices with different frequencies induced by plasma.

Experimental study on aerodynamic characteristics of a high-speed train on viaducts in turbulent crosswinds

In this study, experiments were carried out to investigate aerodynamic characteristics of a high-speed train on viaducts in turbulent crosswinds using a 1:25 scaled sectional model wind-tunnel testing. Pressure measurements of two typical sections, one train-head section and one train-body section, at the windward and leeward tracks were conducted under the smooth and turbulence flows with wind attack angles between −6° and 6°, and the corresponding aerodynamic force coefficients were also calculated using the integral method. The experimental results indicate that the track position affects the mean aerodynamic characteristics of the vehicle, especially for the train-body section. The fluctuating pressure coefficients at the leeward track are more significantly affected by the bridge interference compared to those at the windward track. The effect of turbulence on the train-head section is less than that on the train-body section. Additionally, the mean aerodynamic force coefficients are almost negatively correlated to wind attack angles, which is more prominent for vehicles at the leeward track. Moreover, the lateral force plays a critical role in determining the corresponding overturning moment, especially on the train-body section.

Single-component force balance for the measurement of low-magnitude mean aerodynamic loads

A novel force balance is developed for the measurement of low-magnitude mean aerodynamic forces. The measurement of such small loads is often desired for low Reynolds number wind tunnel experiments, however commercially available options for force measurement do not have high enough sensitivity or accuracy. A force balance is designed to measure forces that range from mN to hundreds of milli-Newtons in magnitude. The sensitivity of the balance is derived theoretically, and the actual value is determined from calibration. The force balance demonstrates both a high degree of linearity, and low hysteresis over the desired load range. The measurement capability of the force balance is validated using measurements of the drag force on a circular cylinder, and the lift force on a square cylinder for Reynolds numbers between 1100 and 10 000. In each case, the force measured by the newly developed force balance shows good agreement with data from literature, and a level of accuracy currently not possible with commercially available sensors for such low-magnitude loads.

Numerical simulation of wind effects on super high-rise buildings considering wind veering with height based on CFD

In wind resistance research involving super high-rise buildings, most studies have concentrated on increases in the wind velocity with height, but Ekman layer effects, inducing wind veering, have rarely been considered. Therefore, the main objective of this paper is to investigate the Ekman layer effects on super high-rise buildings based on computational fluid dynamics (CFD). Numerical simulations were systematically performed on a 3D square cylinder with an aspect ratio of 9:1 using the large eddy simulation (LES) method. The simulation results for three different incident mean wind profiles, including a logarithmic profile without veering, a profile with an inflection point but without veering, and a profile with an inflection point and veering, were compared to illustrate the differences in the wind loads and flow fields with and without wind veering. The results reveal that the proposed method is capable of simulating the wind veering profiles. The local wind pressure distribution on the building is considerably affected by wind veering, especially at the upper portion of the building surface. The effects of wind veering on the mean aerodynamic forces for super high-rise buildings are mainly in the aspect of Y-axis force, X-axis and torsional moment, and the fluctuations of local wind forces and base moments decrease to various degrees.

The effect of aspect ratio on the aerodynamic forces and bending moment for a surface-mounted finite-height cylinder

Wind tunnel experiments were performed at Re = 6.5 × 104 to measure the mean drag and normal forces, mean bending moment, and vortex shedding frequency for surface-mounted finite-height cylinders. The cylinder aspect ratio was varied in small increments between AR = 0.5 and 11, and two different boundary layer thicknesses were used, δ/D = 0.6 and 1.9. Small increments in AR and use of a single Re helped clarify some AR effects for finite cylinders. The data allowed a more precise definition of the familiar critical aspect ratio to be set, based on the behaviour of the mean aerodynamic forces and the point of action of the mean drag force. A second change in behaviour of the aerodynamic forces with AR was also identified; this transition was related to changes in the vortex formation length, the development of the near-wake recirculation zone, and the influence of the two main near-wake vortex structures, with AR. The general effects of increasing δ/D are to lower the force and moment coefficients and Strouhal number, increase the critical AR, and increase the AR where the second transition occurs.

Analysis of Influencing Factors on Aerostatic Stability of Long Span Asymmetric Suspension Bridge

The long span asymmetric suspension bridge is widely constructed in the mountainous terrain. Due to the difference of the structural characteristics, the aerostatic stability of the asymmetric suspension bridge is different from that of the symmetrical structure. In this paper, the effect of the initial wind attack angle, the mean aerodynamic force coefficient, the main cable and the boom wind load, the height difference of the bridge tower support point on the aerostatic stability of the asymmetric suspension bridge are analyzed by incremental internal and external iteration method. The influence degree and mechanism of the above factors on the aerostatic stability of structures are obtained.

Modulation of aerodynamic force on a 2D elliptic body via passive splitter pitching under high turbulence

The mean and fluctuating aerodynamic force on an elliptic body of infinite aspect ratio with hinged splitters were experimentally studied under high incoming turbulence for various angle of attack AoA of the body, Reynolds numbers and splitter length. High-resolution load cell was used to measure the mean and unsteady lift and drag forces of the body; whereas a hotwire anemometry was employed to characterize the incoming turbulence and get insight on the wake flow. Results show that the attached splitters reduce the lift and drag coefficients for AoA well beyond stall. Interestingly, the splitter length did not play a noticeable role on the mean aerodynamic force; this parameter just induced minor effects on the fluctuation counterpart. Such phenomenon appear to be inherently related to the background turbulence levels. Compared to the bare body, the force coefficients exhibit stronger dependence on Reynolds number due to the dynamics induced by the splitter pitching. In general, the force fluctuations are dominated by the natural frequency of the setup under the high turbulence. The joint distribution of the instantaneous lift and drag forces reveals that under sufficiently high AoA, the vortex shedding dominates the force fluctuations along the major axis of the body; whereas the splitters can efficiently dampen the vortex shedding and mitigate the overall force fluctuations.

Three-dimensional instabilities in the wake of a flapping wing at low Reynolds number

We present a stability analysis of a plunging and pitching wing of infinite aspect ratio at low Reynolds number. Four cases are considered by varying the mean pitch angle and the phase shift between pitching and plunging. Each case is studied by performing two dimensional DNS and Floquet stability analysis. The four cases considered display different wake structures resulting in different mean aerodynamic forces. Two cases produce thrust and lift, one case only thrust (with symmetric plunging and pitching) and the remaining case mainly lift (with the highest mean pitch angle). In addition, the latter case displays a period doubling phenomenon, and it is found to be linearly unstable for long wavelengths, with an instability mode that resembles that of mode A found in the wake of cylinders. Other cases, although being linearly stable, present a convective instability at smaller wavelengths. Finally, the unstable case has been studied with a fully 3D DNS to evaluate the effect of the three-dimensionality on the forces. The resulting flow structure is consistent with the linear stability analysis in the near wake. Further downstream nonlinearities lead to a fully 3D wake. Despite this, the aerodynamic forces on the 3D wing are very similar to those obtained in the 2D simulation.

Physiological, aerodynamic and geometric constraints of flapping account for bird gaits, and bounding and flap-gliding flight strategies

Aerodynamically economical flight is steady and level. The high-amplitude flapping and bounding flight style of many small birds departs considerably from any aerodynamic or purely mechanical optimum. Further, many large birds adopt a flap-glide flight style in cruising flight which is not consistent with purely aerodynamic economy. Here, an account is made for such strategies by noting a well-described, general, physiological cost parameter of muscle: the cost of activation. Small birds, with brief downstrokes, experience disproportionately high costs due to muscle activation for power during contraction as opposed to work. Bounding flight may be an adaptation to modulate mean aerodynamic force production in response to (1) physiological pressure to extend the duration of downstroke to reduce power demands during contraction; (2) the prevention of a low-speed downstroke due to the geometric constraints of producing thrust; (3) an aerodynamic cost to flapping with very low lift coefficients. In contrast, flap-gliding birds, which tend to be larger, adopt a strategy that reduces the physiological cost of work due both to activation and contraction efficiency. Flap-gliding allows, despite constraints to modulation of aerodynamic force lever-arm, (1) adoption of moderately large wing-stroke amplitudes to achieve suitable muscle strains, thereby reducing the activation costs for work; (2) reasonably quick downstrokes, enabling muscle contraction at efficient velocities, while being (3) prevented from very slow weight-supporting upstrokes due to the cost of performing ‘negative’ muscle work.