Plants respond to gravity with gravity related waves

Gravity related waves in plants control plant shapes by their velocity, vertical to horizontal velocity ratios, and the stepwise change in velocity from horizontal to vertical. Velocities are measured directly while velocity ratios can be derived from internodal spacings or measurements of velocities. Plant wave frequencies are the same in every direction. The wave proofs are overwhelming with plant communication and ac field interaction as added proof.     

Near-bottom performance of the Acoustic Doppler Velocimeter (ADV) – a comparative study

In a laboratory flume, a comparative study on the near-bottom performance of the Acoustic Doppler Velocimeter (ADV) was conducted. Two different ADV systems were tested for different configurations and two flow velocities (9 cm s⁻¹, 18 cm s⁻¹). The results were compared with synchronous measurements with a Laser Doppler Anemometer (LDA). Near-bottom velocity measurements with the ADV have to be interpreted carefully as the ADV technique underestimates flow velocities in a zone close to the sediment. The height of this zone above the sediment varies with different ADV systems and configurations. The values for nominal sampling volume height (SVH) given by the software often underestimate the true, effective sampling volume heights. Smaller nominal SVH improve the ADV near-bottom performance, but the vertical extent of the zone in which the ADV underestimates flow by more than 20% may be larger than true SVH/2 by a factor of 2 (=true SVH). When the measurement volume approaches the bottom, ADV data quality parameters (signal-to-noise-ratio (SNR) and signal amplitude) exceeding the average ‘open water’ level, are clear indicators that the ADV has begun to underestimate the flow velocity. Unfortunately, this is not a safe indicator for the range of reliable measurements as the ADV may begin to underestimate velocities even with unchanged ‘open water’ data quality parameters. Thus, one can only recommend avoiding measurements below a distance from the bottom that was defined empirically comparing the ADV and the LDA velocity profiles. This distance is 2.5 times nominal sampling volume height for the tested ADV systems and experimental settings.     

Internal and external mass transfer in biofilms grown at various flow velocities

It appears that biofilms arrange their internal structure according to the flow velocity at which they are grown, which affects the internal mass transfer rate and microbial activity. In biofilms grown at various flow velocities we determined the vertical profiles of the local relative effective diffusivity (termed D(l)) at several locations within each biofilm. From these profiles we calculated the surface-averaged relative effective diffusivity (termed D(sa)) at various distances from the bottom and plotted it against these distances. The D(sa) decreased linearly toward the bottom, forming well-defined profiles that were different for each biofilm. The gradients of these profiles were multiplied by the diffusivity of oxygen, zeta = D(w) dD(sa)/dz, and plotted versus the flow velocity at which each biofilm was grown. The gradients were low at flow velocities below 10 cm/s, reached a maximum at a flow velocity of 10 cm/s, and decreased again at flow velocities exceeding 10 cm/s. The existence of a maximum indicates a possibility that two opposing forces were affecting the slope of the profiles. To explain these observations we hypothesized that biofilms, depending on the flow velocity at which they are grown, arrange their internal architecture to control (1) the nutrient transport rate and (2) the mechanical pliability needed to resist the shear stress of the water flowing past them. It appears that biofilms attempt to satisfy the second goal first, to increase their mechanical strength, and that they do so at the expense of the nutrient transfer rate to deeper layers. This strength increase is associated with an increase in biofilm density, which slows down the internal mass transport rate. Biofilms grown at low flow velocities exhibit low density and high effective diffusivity but cannot resist higher shear stress, whereas biofilms grown at higher flow velocities are denser and can resist higher shear stress but have a lower effective diffusivity.     

Aging and physical activity determine cardiac structure and function in the older athlete.

To evaluate the effects of age and physical activity on cardiac structure and function, 45 ultra-endurance athletes were compared with 24 sedentary control subjects. Two-dimensionally guided M-mode echocardiograms and pulsed Doppler studies of left ventricular inflow velocity were obtained. Both older and younger athletes differed from age-similar sedentary control subjects in having lower heart rates (56 vs. 72 beats/min, younger; 53 vs. 74 beats/min, older), larger left ventricular cavities at end diastole (5.4 vs. 4.9 cm younger; 5.4 vs. 4.9 cm older), and higher ratios of early to atrial inflow velocities (2.14 vs. 1.37, younger; 1.32 vs. 0.83, older; all P less than 0.05). Older athletes differed from younger athletes in having higher systolic and diastolic blood pressures (131/79 vs. 122/71 mmHg), greater posterior wall thickness (1.1 vs. 0.9 cm), lower rapid filling velocity (52 vs. 70 cm/s), higher atrial systolic velocity (41 vs. 34 cm/s), and lower early-to-atrial inflow velocity ratios (1.32 vs. 2.14, all P less than 0.05). Thus the aging heart manifests structural and functional changes in response to physical activity that are similar but not identical to those seen in younger subjects. The expected pattern of cardiac alterations normally seen in response to age is modified in the older athlete, suggesting that exercise training, as well as aging, is an effective stimulus in shaping left ventricular structure and function in the older heart.     

Velocity and dominance affect prey capture and microhabitat selection in juvenile Chinook (<Emphasis Type="Italic">Oncorhynchus tshawytscha</Emphasis>)

Habitat selection is an important phenomenon that may greatly affect individual fitness. Using an artificial stream, we examined the relationship between the percentage of prey captured, reactive distance, dominance, and water velocity for juvenile Chinook Salmon (Oncorhynchus tshawytscha) from the Chena River, Alaska, and tested the fitness-based microhabitat selection model of Grossman et al. (Ecol Freshw Fish 11:2–10, 2002). Recent declines in the abundance of Chinook accentuate our need for habitat selection studies on this species. We conducted three experiments: two with single fish (1st N?=?27, fish SL 58–84 mm, 2nd N?=?14, fish SL 49–56 mm) and one with pairs of dominant and subordinate fish (N?=?10 pairs, 64–96 mm, mean difference in SL?=?7 mm). We placed individual or pairs of fish in an artificial flume and recorded reactive distance and the percent prey capture with individual dead brine shrimp (Artemia spp.) as prey. Prey were presented at 10 cm/s velocity intervals ranging from 10 to 60 cm/s; velocities found in the natural habitat. Mean reactive distance in single fish experiments (henceforth SFE) averaged 33 and 29 cm respectively, and was not related to velocity. We detected a negative, curvilinear relationship between velocity and percent prey capture. Holding velocities for juvenile Chinook were significantly lower than prey capture velocities. The Grossman et al. (Ecol Freshw Fish 11:2–10, 2002) model yielded an optimal focal-point velocity prediction of 35 cm/s for juvenile Chinook, however focal-point velocities occupied by juveniles in the Chena River averaged 12 cm/s. Predicted optimal velocities were present in the Chena River; hence, this discrepancy suggests that other factors such as distraction from drifting debris or predation risk influenced habitat selection. There were no differences in reactive distances or holding velocity/capture velocity relationships for dominant and subordinate fish; however, dominants captured significantly more prey than subordinates. Being subordinate resulted in a decrease of 61% in mean percent prey capture (the difference between what was captured by the fish alone versus the difference with a dominant), whereas the mean cost to fish with dominant rank was a 21% decline between the percentage captured alone versus that with a subordinate.     

The role of stimulus movement patterns in the prey catching behavior ofHydromantes genei (Amphibia,Plethodontidae)

Summary The prey catching responses of the Italian salamanderHydromantes genei (Schlegel) were studied both with respect to continuous stimulus movement and to stepwise stimulus movement. The stimulus consisted of a black square measuring 4×4 mm. The responses to both continuous and stepwise stimulus movement were measured at 3 different basic velocities (0.5, 1.25, and 3.125 cm/s), and to stepwise stimulus movement at 6 different step frequencies (0.25, 0.5, 1, 2, 4, 8 steps/s). The experiments showed that within the measured step frequency range, frequencies of 1 and/or 2 steps/s have proved to be the most efficient in eliciting prey catching behavior. The efficiency of both stepwise and continuous stimulus movement increases with an increase of the basic velocity, but the efficiency ratios of stepwise and continuous stimulus movement have an inverse relationship to each other: at low basic velocities, where continuous stimulus movement is less effective, stepwise stimulus movement of the same basic velocity is considerably more effective; at high basic velocities, where continuous stimulus movement is rather effective, the stepwise stimulus movement of the same basic velocity is either not significantly different or proves to be less effective.     

A three‐dimensional numerical model investigation of the impact of submerged macrophytes on flow dynamics in a large fluvial lake

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Vibrational communication along plants by the stink bugs Nezara viridula and Murgantia histrionica

The velocity and spectral characteristics of vibrational signals of Nezara viridula (L.) and Murgantia histrionica (Hahn) (Heteroptera: Pentatomidae) were analyzed as the signals were transmitted through different plants. The velocity parameter of the body vibrations ranges from 0.1 to 1 mm/s. According to the mechanical properties of different substrates, the signal is attenuated or amplified during transmission from the insect's body to the substrate. Attenuation of up to 20 dB occurs during transmission of signals from leaves to stalks or stems. The velocity decrease with distance is below 0.5 dB/cm during transmission through less dense green stems, whereas it ranges between 0.6 and 1.6 dB/cm during transmission through more dense, woody stems. Signal velocity decreases non-linearly with increasing distance from the signal source. Regularly repeated velocity minima (nodes) and maxima (internodes) spaced 10-15 cm apart are characteristic of signal transmission through green plants but not woody stems. The signal velocity at some internodes exceeds the input value for N. viridula but not M. histrionica signals. The relative amplitude of the dominant frequency spectral peak varies with distance, along with overall signal velocity. Variable ratios of spectral peak amplitudes are characteristic for signals recorded at different distances from the source.     

鲢幼鱼在不同水流速度下的暴发-滑行行为策略

在水温（18±1）℃的条件下,以全长（11.70±0.57）cm的鲢（Hypophthalmichthys molitrix）幼鱼为研究对象,测定其不同流速（16.5、22.0、27.5、33.0、38.5、44.0、49.5和55.0 cm/s）下的持续游泳时间、调头百分比和暴发-滑行运动数据。结果表明,鲢的平均持续游泳时间先随流速的增加而减小,后随流速的增加而增加。当流速33.0 cm/s时,平均持续时间最短为118.6min,其中各组试验鱼的最大可持续游泳时间均可达到200min。调头百分比随流速的增加迅速减小,当流速≥44.0 cm/s时,不再出现调头行为。暴发-滑行游泳的平均暴发时间随流速的增加呈上升趋势（y=0.03x+2.64,R2=0.92,P<0.05）。平均对地暴发距离均在30-45 cm,没有显著性差异（P>0.05）,平均绝对暴发距离存在极显著性差异,且随流速的增加而增加（y=4.98x-5.63,R2=0.98,P<0.001）。平均对地暴发速度没有显著性差异（平均对地平均速度和最大速度分别在9-12 cm/s、12-16 cm/s,P>0.05）。平均绝对暴发速度与水流速度之间存在线性正相关关系（平均绝对平均暴发速度:y=0.98x+10.74,R2=1.00,P<0.001;平均绝对最大暴发速度:y=1.02x+13.75,R2=0.99,P<0.001）。研究表明鲢在不同的流速下采取的暴发-滑行行为策略不同。     

Changing risk of predation for a filter-feeding insect along a current velocity gradient

Flume experiments were carried out to examine whether larval blackflies (Simulium ornatum complex, Diptera: Simuliidae) use microhabitats with a highvelocity current to reduce the risk of predation by some of their main predators, viz. larvae of the stoneflies Isoperla grammatica and Diura nanseni (Plecoptera: Perlodidae), and the caddis-fly Rhyacophila nubila (Trichoptera: Rhyacophilidae). We exposed blackfly larvae to four different current velocities and measured their feeding rate using dye particles. The maximum feeding rate was recorded at intermediate velocities (18.8 and 36.2 cm/s), whereas at low (7.3 cm/s) and high (53.3 cm/s) velocities, the feeding rate was reduced. In separate experiments, we investigated the behaviour and attack success of the different predator species. The two perlodids showed a similar hunting behaviour, which was significantly less successful at higher velocities. Drift of the perlodids from the experimental arena resulted in reduced encounter and attack rates, especially in I. grammatica, which had completely lost efficiency at 36.2 cm/s. R. nubila had a slower mode of hunting and was unaffected by current speed within the velocity gradient studied. Drift in Rhyacophila was rare. Observations on the behaviour of blackfly larvae were performed in the same experiments. The larvae showed no apparent ability to sense the presence of the predators except when these disrupted the flow pattern or were in physical contact, which often resulted in aggressive defence, though without effect on the predators. Escape of blackfly larvae by drift did occur, but this was no more common than being captured. In a current velocity gradient, blackfly larvae showed a weak preference for increasing velocities. Thus, at velocities between 7 and 54 cm/s, blackfly larvae appear to select microhabitats with high current velocities, despite a reduction in feeding optimality, thereby easing the predation impact from perlodids, though not from Rhyacophila. The study demonstrates the importance of microhabitat selection by blackfly larvae both for efficient feeding and predator avoidance.     

Postexercise physiology and repeat performance behaviour of free-swimming smallmouth bass in an experimental raceway

We studied postexercise physiology and behaviour of smallmouth bass (Micropterus dolomieu) that voluntarily ascended experimental raceways of varying length (20-50 m) against water velocities ranging from 8 to 120 cm/s. Our first objective was to link mean swimming speed to metabolism using patterns in postexercise muscle glycogen, muscle lactate, and plasma lactate. Our second objective was to examine several behavioural indices (attempt rate, success rate, and recovery time between an ascent and a subsequent attempt) and determine whether patterns in these data reflected those from the physiological measurements. Postexercise muscle glycogen and plasma lactate data suggest that smallmouth bass powered swimming speeds up to 70-80 cm/s using energy from aerobic processes. However, lactate did not begin to accumulate in the white muscle until speeds in excess of 120-130 cm/s were reached. The behavioural parameters measured did not indicate the presence of a physiological threshold at 70-80 cm/s; however, patterns in all factors changed appreciably when fish maintained speeds in excess of 120-130 cm/s. Therefore, it is clear that behaviour and physiology are tightly linked in this species and that maximum aerobic swimming capacity may not limit performance (or re-performance) during short-duration swims.     

A pulsed wire probe for the measurement of velocity and flow direction in slowly moving air

This report describes the theory and operation of a pulsed-probe anemometer designed to measure steady three-dimensional velocity fields typical of pulmonary tracheo-bronchial airflows. Local velocities are determined by measuring the transport time and orientation of a thermal pulse initiated at an upstream wire and sensed at a downstream wire. The transport time is a reproducible function of velocity and the probe wire spacing, as verified by a theoretical model of convective heat transfer. When calibrated the anemometer yields measurements of velocity accurate to +/- 5 percent and resolves flow direction to within 1 deg at airspeeds greater than or equal to 10 cm/s. Spatial resolution is +/- 0.5 mm. Measured flow patterns typical of curved circular pipes are included as examples of its application.     

Velocity gradients and turbulence around macrophyte stands in streams

1. Submerged macrophytes strongly modify water flow in small lowland streams. The present study investigated turbulence and vertical velocity gradients using small hot-wire anemometers in the vicinity and within the canopies of four macrophyte species with the objective of evaluating: (a) how plant canopies influence velocity gradients and shear force on the surfaces of the plants and the stream bed; and (b) how the presence and morphology of plants influence the intensity of turbulence. 2. Water velocity was often relatively constant with water depth both outside and inside the plant canopies, but the velocity declined steeply immediately above the unvegetated stream bed. Steep vertical velocity profiles were also observed in the transition to the surface of the macrophyte canopy of three of the plant species forming a dense shielding structure of high biomass. Less steep vertical profiles were observed at the open canopy surface of the fourth plant species, growing from a basal meristem and having the biomass more homogeneously distributed with depth. The complex distribution of hydraulic roughness between the stream bed, the banks and the plants resulted in velocity profiles which often fitted better to a linear than to a logarithmic function of distance above the sediment and canopy surfaces. 3. Turbulence increased in proportion to the mean flow velocity, but the slope of the relationships differed in a predictable manner among positions outside and inside the canopies of the different species, suggesting that their morphology and movements influenced the intensity of turbulence. Turbulence was maintained in the attenuated flow inside the plant canopies, despite estimates of low Reynolds numbers, demonstrating that reliable evaluation of flow patterns requires direct measurements. The mean velocity inside plant canopies mostly exceeded 2 cm s^??1 and turbulence intensity remained above 0.2 cm s^??1, which should be sufficient to prevent carbon limitation of photosynthesis in CO₂-rich streams, while plant growth may benefit from the reduced physical disturbance and the retention of nutrient-rich sediment particles. 4. Flow patterns were highly reproducible within canopies of the individual species despite differences in stand size and location among streams. We propose that individual plant stands are suitable functional units for analysing the influence of submerged macrophytes on flow patterns, retention of particles and biological communities in lowland streams.     

Resuspension studies in cylindrical microcosms: Effects of stirring velocity on the dynamics of redox sensitive elements in a coastal sediment

Effects of resuspension on the release of dissolved, redox sensitive elements (Fe, Mn) was studied in cylindrical microcosms. Effects from changing water stirring velocity in sediment pools were evaluated through measurements of pore water profiles of dissolved Mn, Fe and redox potential. Mn was a good natural marker to follow such effects. At current velocities below the threshold velocity for resuspension (37 cm s-1), Mn release rates to overlying water were 100 times higher compared to steady-state values. Pulse increases in Mn concentration were the result of convective currents inside flow chambers. These results were strongly supported by measurements of Eh profiles in the sediment pore water. Furthermore, impacts from increasing stirring velocity were found down to 1.9 cm depth below the resuspended layer of sediment.     

Rotation of bacterial flagella as driven by cytomembrane streaming

Theoretical estimates are given to check the possibility that flagellar rotation of bacteria is driven by viscous forces exerted from a streaming cytomembrane matrix to the basal structure of the flagellum.For different regimes of cytomembrane streaming, i.e. for circular, shearing and uniform linear motion of the membrane matrix past the basal ring of the flagellum, the velocity of streaming is computed that will yield the necessary mechanical torque for rotation of a helical flagellum in a watery medium.It is shown that in the range of surface viscosities determined for phospholipid monolayers the required velocities of cytomembrane streaming may be expected in the range of 3 μm/s to 60 μm/s. Since streaming velocities of the latter order of magnitude have been observed in protozoan membrane, efforts appear warranted to demonstrate experimentally the existence of cytomembrane streaming in bacteria and to characterize the surface viscosity of their cytomembrane.     

Electric-field effects on gravikinesis in Paramecium

Equilibrated Paramecium caudatum cells exposed to a constant DC gradient reorient with their depolarized anterior ends toward the cathode (galvanotaxis). Voltage gradients were applied to cells swimming either horizontally or vertically. Their velocity and orientation were recorded and compared to unstimulated cells. The DC field increased the horizontal velocity (= reference) up to 175% (galvanokinesis). Swimming velocities saturated after 1 min and were unchanged during the following 4 min. The upward and downward swimming velocities of stimulated cells were below those of horizontal swimmers. The difference in vertical rates (determining gravikinesis) was independent of variations in absolute velocity. Normalization of vertical velocities to horizontal velocities (= 100%) separated DC-field dependent changes from gravity-induced changes in velocities. A weak voltage gradient (0.3 V/cm) was most effective in raising downward gravikinesis up to threefold (-202 m/s) above the unstimulated reference (-66 m/s) and to change sign of gravikinesis in upward swimmers (-43 m/s +33 m/s). We conclude that DC-field stimulation is equivalent to a depolarizing bias on gravikinetic responses of Paramecium. The stimulation does not directly interfere with mechanoreception, but modulates somatic Ca²⁺ entry to induce contraction of the cell soma. This presumably affects the gating of gravisensory transduction channels.     

Role of climate and agricultural practice in determining matter discharge into large,shallow Lake Võrtsjärv,Estonia

Understanding the dynamics of fine sediment transport across the upper intertidal zone is critical in managing the erosion and accretion of intertidal areas, and in managed realignment/estuarine habitat recreation strategies. This paper examines the transfer of sediments between salt marsh and mudflat environments in two contrasting macrotidal estuaries: the Seine (France) and the Medway (UK), using data collected during two joint field seasons undertaken by the Anglo-French RIMEW project (Rives-Manche Estuary Watch). High-resolution ADCP, Altimeter, OBS and ASM measurements from mudflat and marsh surface environments have been combined with sediment trap data to examine short-term sediment transport processes under spring tide and storm flow conditions. In addition, the longer-term accumulation of sediment in each salt marsh system has been examined via radiometric dating of sediment cores. In the Seine, rapid sediment accumulation and expansion of salt marsh areas, and subsequent loss of open intertidal mudflats, is a major problem, and the data collected here indicate a distinct net landward flux of sediments into the marsh interior. Suspended sediment fluxes are much higher than in the Medway estuary (averaging 0.09 g/m³/s), and vertical accumulation rates at the salt marsh/mudflat boundary exceed 3 cm/y. Suspended sediment data collected during storm surge conditions indicate that significant in-wash of fine sediments into the marsh interior can occur during (and following) these high-magnitude events. In contrast to the Seine, the Medway is undergoing erosion and general loss of salt marsh areas. Suspended sediment fluxes are of the order of 0.03 g/m³/s, and the marsh system here has much lower rates of vertical accretion (sediment accumulation rates are ca. 4 mm/y). Current velocity data for the Medway site indicate higher velocities on the ebb tide than occur on the flood tide, which may be sufficient to remobilise sediments deposited on the previous tide and so force net removal of material from the marsh.     

Effect of Water Velocity on Hydroponic Phytoremediation of Metals

The influence of flow velocity on the uptake of cadmium, copper, lead, and zinc by hydroponically grown soft stem bulrush (Scirpus validus) was investigated. The roots of the plants were exposed to a continually recycled, nutrient enriched, synthetic stormwater. Plants were divided into groups and the roots of each group exposed to different but constant water velocities. The metal concentrations in the roots and stems were compared after three weeks. Metal accumulation in roots was increased for water velocities between 1.3 and 4.0 cm s^?1. In a second experiment, the roots of all plants were exposed to a single velocity and the root and stem metal concentrations were determined as a function of time. Metal concentrations in the roots approached a constant value after three weeks. After this time, accumulation of metals depends upon root growth. The results suggest that long-term accumulation by the roots of hydroponic Scirpus validus can be increased by increasing water velocity, which implies that floating islands with movement will retain more metals from the water column.     

Effect of shear stress on efferent lymph-derived lymphocytes in contact with activated endothelial monolayers

L.ymphocyte interactions with endothelial cells in microcirculation are an important regulatory step in the delivery of lymphocytes to peripheral sites of inflammation. In normal circumstances, the predicted wall shear stress in small venules range from 10 to 100 dyn/cm2. Attempts to measure the adhesion of lymphocytes under physiologic conditions have produced variable results, suggesting the importance of studying biologically relevant migratory lymphocytes. To quantify the effect of shear stress on these migratory lymphocytes, we used lymphocytes obtained from sheep efferent lymph ducts, defined as migratory cells, to perfuse sheep endothelial monolayers under conditions of flow. Quantitative cytomorphometry was used to distinguish cells in contact with the endothelial monolayers from cells in the flow stream. As expected, migratory cells in contact with the normal endothelial monolayer demonstrated flow velocities less than the velocity of cells in the adjacent flow stream. The flow velocities of these efferent lymphocytes were independent of cell size. To model the inflammatory microcirculation, lymphocytes were perfused over sequential endothelial monolayers to directly compare the velocity of cells in contact with cytokine-activated and unactivated control monolayers. The tumor necrosis factor and interleukin-1-activated endothelial monolayers marginally decreased cell velocities at 1.2 dyn/cm2 (3.6%), but significantly reduced cell velocities 0.3 dyn/cm2 (27.4%; P < 0.05). Similarly, the fraction of statically adherent lymphocytes decreased as shear stress increased to 1.2 dyn/cm2. These results suggest that typical wall shear stress in small venules. of the order of 20 dyn/cm2, are too high to permit adhesion and transmigration of migratory lymphocytes. Additional mechanisnis must be present in vivo to facilitate lymphocyte transmigration in the inflammatory microcircu-     

Force platforms as ergometers.

Walking and running on the level involves external mechanical work, even when speed averaged over a complete stride remains constant. This work must be performed by the muscles to accelerate and/or raise the center of mass of the body during parts of the stride, replacing energy which is lost as the body slows and/or falls during other parts of the stride. External work can be measured with fair approximation by means of a force plate, which records the horizontal and vertical components of the resultant force applied by the body to the ground over a complete stride. The horizontal force and the vertical force minus the body weight are integrated electronically to determine the instantaneous velocity in each plane. These velocities are squared and multiplied by one-half the mass to yield the instantaneous kinetic energy. The change in potential energy is calculated by integrating vertical velocity as a function of time to yield vertical displacement and multiplying this by body weight. The total mechanical energy as a function of time is obtained by adding the instantaneous kinetic and potential energies. The positive external mechanical work is obtained by adding the increments in total mechanical energy over an integral number of strides.