Mechanical Energy Fluctuations Research Articles

Mechanical energy fluctuation in lower limbs during walking in participants with and without total hip replacement.

Mechanical energy fluctuation of the segments of lower limbs during walking has not been fully investigated. It was hypothesized that the segments may work as a pendulum, i.e. the kinetic and potential energies exchanged out of phase. This study aimed to investigate energy changes and recovery during gait in hip replacement patients. The gait data for 12 participants with total hip replacement and 12 age-matched control was compared. The kinetic, potential and rotative energies for whole lower limb and thigh, calf and foot, were calculated. The effectiveness of a pendulum effect was analysed. Gait parameters (speeds and cadence) were calculated. The results showed that the thigh had significant effectiveness as a pendulum during gait with energy recovery coefficient of approximately 40% while the calf and foot were less like a pendulum during gait. In comparison, energy recoveries of lower limbs in the two groups were not significantly different. If the pelvis was considered as an approximate to the centre of mass, however, the control group had a higher energy recovery than total-hip-replacement group by roughly 10%. This study concluded that, unlike centre of mass energy recovery, the mechanical energy recovery mechanism in the lower limbs during walking is not affected after total hip replacement.

Biomechanical responses of Nordic walking in people with Parkinson's disease.

In healthy adults, Nordic walking (NW) is known to increase the external mechanical energy fluctuations, though the external work is unaltered due to an improved pendulum-like recovery in comparison with free walking (FW). We aimed to compare mechanical, pendulum-like, and spatiotemporal parameters of gait at different speeds with and without NW poles in people with Parkinson's disease and healthy controls. The study included 11 people (aged 65.6±7.0years) with idiopathic Parkinson's disease, scoring between 1 and 1.5 on the Hoehn and Yahr scale (H&Y), and nine healthy controls (aged 70.0±5.6years). All the people were experienced Nordic walkers. Walking tests were performed at 1.8kmh-1 and 4.7kmh-1 , on eight 3D force platforms on a walkway. We found greater pendulum-like energy recovery (p<0.05) in the Parkinson group during NW than in FW, while external mechanical work remained similar (p>0.05). People with Parkinson's disease showed a major increase in vertical and forward energy fluctuations using poles than in healthy controls. In addition, the Parkinson group showed increased stride frequency and reduced stride length compared to controls in the NW and FW conditions. Our findings partly justify the lower walking economy in Parkinson's disease due to reduced pendulum-like mechanism at commonly used speeds. NW alters gait mechanics similarly in Parkinson group and healthy control, increasing the total mechanical work. Therefore, NW can be a compelling strategy for rehabilitation because of its potential for improving functional mobility, increasing pendulum-like mechanism in Parkinson's disease.

Versatile Titanates: Classification, Property, Preparation, and Sustainable Energy Catalysis

AbstractGlobal warming, energy deficiency, and environmental deterioration triggered by burning fossil fuels, may severely impair economic development and human life and health. Green solar power, mechanical energy, and temperature fluctuation heat energy abound in nature and are readily accessible. Thanks to various appealing characteristics, titanates are universally employed to harvest these sustainable energy sources to produce renewable fuels through photocatalysis, piezocatalysis, and pyrocatalysis, alleviating above serious issues. In this review, the research progress in energy catalysis driven by solar light, mechanical stress, and temperature fluctuation over titanates is comprehensively described. It starts with the classification and introduction of diverse titanates. Next, the main methods for preparing titanates are introduced. Highlighted are titanates acting as cocatalysts, photocatalysts, piezocatalysts, and pyrocatalysts to participate in water splitting reaction for H2 evolution and atmospheric CO2 reduction conversion into CO or hydrocarbons. In particular, the material modification strategies for improving photocatalytic performance are discussed. Finally, the rosy prospects of the future development of energy catalysis application for titanates are looked into.

Mechanical energy and propulsion mechanics in roller-skiing double-poling at increasing speeds.

ObjectivesThe aim of this study was to examine the effect of speed on mechanical energy fluctuations and propulsion mechanics in the double-poling (DP) technique of cross-country skiing.MethodsKinematics and dynamics were acquired while fourteen male skiers performed roller-skiing DP on a treadmill at increasing speeds (15, 21 and 27 km∙h-1). Kinetic (Ekin), potential (Epot), and total (Ebody) body mechanical energy and pole power (Ppole) were calculated. Inverse dynamics was used to calculate arm power (Parm). Trunk+leg power (PT+L) was estimated, as was the power associated with body movements perpendicular to goal-direction ().ResultsEkin and Epot fluctuated out-of-phase throughout the cycle, at first sight indicating that pendulum-like behaviour occurs partly in DP. However, during the swing phase, the increase in Epot (body heightening) was mainly driven by positive PT+L, while the decrease in Ekin was lost to rolling friction, and during the poling phase, considerable positive Parm generation occurs. Thus, possible exchange between Ekin and Epot seem not to occur as directly and passively as in classic pendulum locomotion (walking). During the poling phase, fluctuated out-of-phase with Ppole, indicating a transfer of body energy to Ppole. In this way, power generated by trunk+leg mainly during the swing phase (body heightening) can be used in the poling phase as pole power. At all speeds, negative PT+L occurred during the poling phase, suggesting energy absorption of body energy not transferred to pole power. Thus, DP seem to resemble bouncing ball-like behaviour more than pendulum at faster speeds. Over the cycle, Parm contribution to Ppole (external power) was 63% at 15 km∙h-1 and 66% at 21 and 27 km∙h-1, with the remainder being PT+L contribution.ConclusionsWhen speed increases in level DP, both power production and absorption by trunk+leg actions increase considerably. This enhanced involvement of the legs at faster speeds is likely a prerequisite for effective generation of pole power at high speeds with very short poling times. However, the relative trunk+leg power contribution did not increase at the speeds studied here.

When mechanical work meets energetics: Obese versus non-obese children walking.

What is the central question of this study? The aim was to compare the cost of transport and mechanical work between obese and non-obese children at different walking speeds. What is the main finding and its importance? Our data show that the cost of transport, mechanical efficiency and work are similar and directly mass dependent in obese and non-obese children. The optimal walking speed (most economical walking speed) is reduced in obese children. Although studies have shown the influence of gait biomechanics on the metabolic economy in obese adults and adolescents, little is known regarding obese children. We compared the metabolic cost of transport, apparent mechanical efficiency and gait biomechanics (assessed by mechanical energy fluctuations) in obese children (n=12; mean±SD: 8.6±0.51 years of age, 1.38±0.04m, 44.6±6.65kg, 24.1±3.50kgm-2 ) and age- and sex-matched non-obese children (n=12, 7.8±0.90 years of age, 1.31±0.08m, 26.8±2.24kg, 16.4±1.40kgm-2 ) while walking at different speeds (from 1 to 5kmh-1 ) on a treadmill. We found that the mechanical efficiency was higher at 3kmh-1 compared with the remaining speeds for both groups (P<0.05). Although the internal mechanical work has been greater in obese compared with non-obese children at 4 and 5kmh-1 , the external, total mechanical work and the mechanical efficiency remained similar between obese and non-obese children at all speeds. Likewise, the cost of transport was similar in the two groups, although the optimal walking speed was an average of 0.4kmh-1 slower in obese children. Clearly, these results show that the walking economy is associated with the total mechanical work in obese and non-obese children. Finally, the reduced functional mobility in obese children observed in previous studies seems to be associated with a reduction in optimal walking speed in comparison to non-obese children.

Running Stride Length And Rate Are Changed And Mechanical Efficiency Is Preserved After Cycling In Middle-Level Triathletes

Although cycling impairs the subsequent metabolic cost and performance of running in some triathletes, the consequences on mechanical efficiency (Eff) and kinetic and potential energy fluctuations of the body center of mass are still unknown. The aim of this study was to investigate the effects of previous cycling on the cost-of-transport, Eff, mechanical energy fluctuations (Wtot), spring stiffness (Kleg and Kvert) and spatiotemporal parameters. Fourteen middle-level triathletes (mean ± SD: maximal oxygen uptake, dot{{rm{V}}}O2max = 65.3 ± 2.7 ml.kg−1.min−1, age = 30 ± 5 years, practice time = 6.8 ± 3.0 years) performed four tests. Two maximal oxygen uptake tests on a cycle ergometer and treadmill, and two submaximal 20-minute running tests (14 km.h−1) with (prior-cycling) and without (control) a previous submaximal 30-minute cycling test. No differences were observed between the control and post-cycling groups in Eff or Wtot. The Eff remains unchanged between conditions. On the other hand, the Kvert (20.2 vs 24.4 kN.m−1) and Kleg (7.1 vs 8.2 kN.m−1, p < 0.05) were lower and the cost-of-transport was higher (p = 0.018, 3.71 vs 3.31 J.kg−1.m−1) when running was preceded by cycling. Significantly higher stride frequency (p < 0.05, 1.46 vs 1.43 Hz) and lower stride length (p < 0.05, 2.60 vs 2.65 m) were observed in the running after cycling condition in comparison with control condition. Mechanical adjustments were needed to maintain the Eff, even resulting in an impaired metabolic cost after cycling performed at moderate intensity. These findings are compatible with the concept that specific adjustments in spatiotemporal parameters preserve the Eff when running is preceded by cycling in middle-level triathletes, though the cost-of-transport increased.

Beyond bouncy gaits: The role of multiscale compliance in skeletal muscle performance.

McNeill Alexander demonstrated that compliant tendons could improve locomotor performance by decoupling muscle length changes from joint movements and mechanical energy fluctuations. This was revolutionary for our understanding of animal locomotion, but also highlighted the limitations of our understanding of the contractile performance of muscle under the dynamic conditions relevant to movement. This review addresses the potential for biological compliance to not only alter the demands on muscle but also fundamentally change contractile performance. Compliance exists across all spatial scales within the muscle. Molecule scale compliance is observed in the thin filament and the cytoskeletal protein titin likely acts as an activation-dependent variable-stiffness spring. Larger scale connective tissue compliance is found not only in tendons but also the more structurally complex extracellular matrix and aponeuroses. The interaction of the compliance in these structures with the contractile elements of muscle, and the variation in this interaction across physiological conditions, appears to explain muscle phenomena central to locomotion but not readily explained by the crossbridge and sliding filament theories, such as history dependence, the energetics of cyclical contractions, the nonlinear effect of activation level on muscle performance and the effect of age on muscle and locomotor capacity.

Mechanical energy fluctuations in granular chains: the possibility of rogue fluctuations or waves.

The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.

Biomechanics of spontaneous overground walk-to-run transition

The purpose of the present study was to describe the biomechanics of spontaneous walk-to-run transitions (WRTs) in humans. After minimal instructions, 17 physically active subjects performed WRTs on an instrumented runway, enabling measurement of speed, acceleration, spatiotemporal variables, ground reaction forces and 3D kinematics. The present study describes (1) the mechanical energy fluctuations of the body centre-of-mass (BCOM) as a reflection of the whole-body dynamics and (2) the joint kinematics and kinetics. Consistent with previous research, the spatiotemporal variables showed a sudden switch from walking to running in one transition step. During this step there was a sudden increase in forward speed, the so-called speed jump (0.42 m s(-1)). At total body level, this was reflected in a sudden increase in energy of the BCOM (0.83±0.14 J kg(-1)) and an abrupt change from an out-of-phase to an in-phase organization of the kinetic and potential energy fluctuations. During the transition step a larger net propulsive impulse compared with the preceding and following steps was observed due to a decrease in the braking impulse. This suggests that the altered landing configuration (prepared during the last 40% of the preceding swing) places the body in an optimal configuration to minimize this braking impulse. We hypothesize this configuration also evokes a reflex allowing a more powerful push off, which generates enough power to complete the transition and launch the first flight phase. This powerful push-off was also reflected in the vertical ground reaction force, which suddenly changed to a running pattern.

Development of a Novel Fully Passive Treadmill Training Paradigm for Lower Limb Therapeutic Intervention

A simulation based study of a completely new form of body-weight supported treadmill training (BWSTT) technique which is fully passive in nature is presented in this paper. The approach does not require any powered means at the lower limbs and is implemented using a combination of coordinated joint locking/unlocking and flexible torque transfer mechanisms. The hip extension pertaining to the stance phase of the gait cycle is achieved through the stance foot being literally dragged by the treadmill belt while the required manoeuvring of the trunk is expected to be accomplished by the voluntary arm-support from the subject. The swing phase, on the other hand, is initiated through appropriately coupling the swing knee with the contralateral extending hip and eventually achieve full knee extension through switching the treadmill speed to a lower value. Considering adequate support from the able arms, the process effectively turns the frictional force at the foot-treadmill belt interface into an agent causing the required whole body mechanical energy fluctuation during the gait cycle.The simulation platform consists of a dynamic planer (sagittal) full body humanoid model along with the treadmill model developed within a CAD based software environment interfaced with passive viscoelastic joint properties implemented in Simulink. The voluntary upper body effort as well as control of the gait cycle are also developed within MATLAB/Simulink environment. The gait cycle generated using the new concept is thoroughly investigated through this simulation study.

Development of a Novel Fully Passive Treadmill Training Paradigm for Lower Limb Therapeutic Intervention

A simulation based study of a completely new form of body-weight supported treadmill training BWSTT technique which is fully passive in nature is presented in this paper. The approach does not require any powered means at the lower limbs and is implemented using a combination of coordinated joint locking/unlocking and flexible torque transfer mechanisms. The hip extension pertaining to the stance phase of the gait cycle is achieved through the stance foot being literally dragged by the treadmill belt while the required manoeuvring of the trunk is expected to be accomplished by the voluntary arm-support from the subject. The swing phase, on the other hand, is initiated through appropriately coupling the swing knee with the contralateral extending hip and eventually achieve full knee extension through switching the treadmill speed to a lower value. Considering adequate support from the able arms, the process effectively turns the frictional force at the foot-treadmill belt interface into an agent causing the required whole body mechanical energy fluctuation during the gait cycle. The simulation platform consists of a dynamic planer sagittal full body humanoid model along with the treadmill model developed within a CAD based software environment interfaced with passive viscoelastic joint properties implemented in Simulink. The voluntary upper body effort as well as control of the gait cycle are also developed within MATLAB/Simulink environment. The gait cycle generated using the new concept is thoroughly investigated through this simulation study.

Inefficient use of inverted pendulum mechanism during quadrupedal walking in the Japanese macaque

In animal walking, the gravitational potential and kinetic energy of the center of mass (COM) fluctuates out-of-phase to reduce the energetic cost of locomotion via an inverted pendulum mechanism, and, in canine quadrupedal walking, up to 70% of the mechanical energy can be recovered. However, the rate of energy recovery for quadrupedal walking in primates has been reported to be comparatively lower. The present study analyzed fluctuations in the potential and kinetic energy of the COM during quadrupedal walking in the Japanese macaque to clarify the mechanisms underlying this inefficient utilization of the inverted pendulum mechanism in primates. Monkeys walked on a wooden walkway at a self-selected speed, and ground reaction forces were measured, using a force platform, to calculate patterns of mechanical energy fluctuation and rates of energy recovery. Our results demonstrated that rates of energy recovery for quadrupedal walking in Japanese macaques were approximately 30-50%, much smaller than those reported for dogs. Comparisons of the patterns of mechanical energy fluctuation suggested that the potential and kinetic energies oscillated relatively more in-phase, and amplitudes did not attain near equality during quadrupedal walking in Japanese macaques, possibly because of greater weight support (reaction force) of the hindlimbs and more protracted forelimbs at touchdown in the Japanese macaque, two of the three commonly accepted locomotor characteristics distinguishing primates from non-primate mammals.

Quantum force turns repulsive

The experimental verification that a bizarre quantum effect — the Casimir force — can manifest itself in its repulsive form is pivotal not only for fundamental physics but also for nanotechnology. Space is not completely empty; the vacuum teems with quantum mechanical energy fluctuations able to generate an attractive force between objects that are very close to each other. This 'Casimir–Lifshitz' force can cause static friction or 'stiction' in nanomachines, which must be strongly reduced. Until now only attractive interactions have been reported but in theory, if vacuum is replaced by certain media, Casimir–Lifshitz forces should become repulsive. This has now been confirmed experimentally. Repulsion, weaker than the attractive force, was measured in a carefully chosen system of interacting materials immersed in fluid. The magnitude of both forces increases as separation decreases. The repulsive forces could conceivably allow quantum levitation of objects in a fluid and lead to new types of switchable nanoscale devices with ultra-low static friction. Levitation depends only on the dielectric properties of the various materials. The cover illustrates repulsion between a tiny gold sphere and a silica substrate (left). Replace the silica with gold (right), and the force becomes attractive.

High-speed gallop locomotion in the Thoroughbred racehorse. II. The effect of incline on centre of mass movement and mechanical energy fluctuation

During locomotion on an incline, mechanical work is performed to move an animal up the slope and increase the potential energy (PE) of the trunk and hence the centre of mass (CoM). Thus, at a given speed the total net mechanical work increases with the PE of the animal. In this study we investigate the mechanical energy (ME) fluctuations and the mechanical cost of transport (MCT) in six horses galloping up a range of gradients. We captured trunk movement with a six degrees-of-freedom inertial sensor mounted over the dorsal spinous process of the fourth to sixth thoracic vertebrae of the horse. Footfall timings were measured using a previously validated system of limb-mounted accelerometers. Speed was measured using a Global Positioning System (GPS) data logger. A track survey provided detailed incline information for the track. Linear (craniocaudal, mediolateral and dorsoventral) and rotational (roll, pitch and heading) kinematic parameters (displacement, velocity and acceleration) were calculated at speeds ranging from 9.0 to 12.0 m s(-1) during routine training over a range of inclines. Estimates of ME fluctuations and the MCT were made. Results showed the effect of incline on trunk motion during galloping was small. Increases in linear mechanical work and MCT were primarily explained by an increase in the work required to move the animal up the slope (and increase the PE of the CoM). Within the stride the majority of the work was performed during hindlimb stance. Our results have provided new insights into how horses power uphill locomotion.

Mechanics of dog walking compared with a passive, stiff-limbed, 4-bar linkage model, and their collisional implications

Here, we present a simple stiff-limbed passive model of quadrupedal walking, compare mechanics predicted from the model with those observed from forceplate measurements of walking dogs and consider the implications of deviation from model predictions, especially with reference to collision mechanics. The model is based on the geometry of a 4-bar linkage consisting of a stiff hindleg, back, foreleg and the ground between the hind and front feet. It uses empirical morphological and kinematic inputs to determine the fluctuations in potential and kinetic energy, vertical and horizontal forces and energy losses associated with inelastic collisions at each foot placement. Using forceplate measurements to calculate centre of mass motions of walking dogs, we find that (1) dogs may, but are not required to, spend periods of double support (one hind- and one forefoot) agreeing with the passive model; (2) legs are somewhat compliant, and mechanical energy fluctuates during triple support, with mechanical energy being lost directly after hindfoot placement and replaced following forefoot placement. Footfall timings and timing of mechanical energy fluctuations are consistent with strategies to reduce collisional forces, analogous to the suggested role of ankle extension as an efficient powering mechanism in human walking.

Mechanical energy fluctuations during hill walking: the effects of slope on inverted pendulum exchange

Humans and other animals exchange gravitational potential energy (GPE) and kinetic energy (KE) of the center of mass during level walking. How effective is this energy exchange during downhill and uphill walking? Based on previous reports and our own reasoning, we expected that during downhill walking, the possibility for mechanical energy exchange would be enhanced and during uphill walking, the possibility for exchange would be reduced. We measured the fluctuations of the mechanical energies for five men and five women walking at 1.25 m s(-1). Subjects walked on the level, downhill, and uphill on a force measuring treadmill mounted at 3 degrees, 6 degrees and 9 degrees. We evaluated energy exchange during the single support period based on the GPE and KE fluctuation factors of phase relationship, relative magnitude and extent of symmetry. As expected, during level walking, the GPE and KE curves were out of phase, of similar magnitude, and nearly mirror images so that the fluctuations in combined (GPE+KE) energy were attenuated. During downhill walking, the fluctuations in the combined energy of the center of mass were smaller than those on the level, i.e. mechanical energy exchange was more effective. During uphill walking, the fluctuations in the combined energy of the center of mass were larger than those on the level, i.e. mechanical energy exchange was less effective. Mechanical energy exchange occurred during downhill, level and uphill walking, but it was most effective during downhill walking.

Centre of mass movement and mechanical energy fluctuation during gallop locomotion in the Thoroughbred racehorse

During locomotion cyclical interchange between different forms of mechanical energy enhances economy; however, 100% efficiency cannot be achieved and ultimately some mechanical work must be performed de novo. There is a metabolic cost associated with fluctuations in mechanical energy, even in the most efficient animals. In this study we investigate the exchanges between different forms of mechanical energy involved in high-speed gallop locomotion in Thoroughbred race horses during over-ground locomotion using innovative, mobile data collection techniques. We use hoof-mounted accelerometers to capture foot contact times, a GPS data logger to monitor speed and an inertial sensor mounted over the dorsal spinous processes of the fourth to sixth thoracic vertebrae (the withers) of the horse to capture trunk movement with six degrees of freedom. Trunk movement data were used to estimate the movement of the centre of mass (CoM). Linear (craniocaudal, mediolateral and dorsoventral) and rotational (roll, pitch and heading) kinematic parameters (displacement, velocity and acceleration) were calculated for seven horses at gallop speeds ranging from 7 to 17 m s(-1) during their regular training sessions. These were used to estimate external mechanical energy (potential energy and linear kinetic energy of the CoM) as well as selected components of internal energy (angular kinetic energy). Elastic energy storage in the limbs was estimated from duty factor, sine wave assumptions and published leg stiffness values. External mechanical energy changes were dominated by changes in craniocaudal velocity. Potential energy change, which was in phase with craniocaudal energy during the front limb stances, was small. Elastic energy storage in the limbs was small compared to the overall amplitude of fluctuation of external mechanical energy. Galloping at high speeds does not therefore fit classical spring mass mechanics.

Tuataras and salamanders show that walking and running mechanics are ancient features of tetrapod locomotion.

The lumbering locomotor behaviours of tuataras and salamanders are the best examples of quadrupedal locomotion of early terrestrial vertebrates. We show they use the same walking (out-of-phase) and running (in-phase) patterns of external mechanical energy fluctuations of the centre-of-mass known in fast moving (cursorial) animals. Thus, walking and running centre-of-mass mechanics have been a feature of tetrapods since quadrupedal locomotion emerged over 400 million years ago. When walking, these sprawling animals save external mechanical energy with the same pendular effectiveness observed in cursorial animals. However, unlike cursorial animals (that change footfall patterns and mechanics with speed), tuataras and salamanders use only diagonal couplet gaits and indifferently change from walking to running mechanics with no significant change in total mechanical energy. Thus, the change from walking to running is not related to speed and the advantage of walking versus running is unclear. Furthermore, lumbering mechanics in primitive tetrapods is reflected in having total mechanical energy driven by potential energy (rather than kinetic energy as in cursorial animals) and relative centre-of-mass displacements an order of magnitude greater than cursorial animals. Thus, large vertical displacements associated with lumbering locomotion in primitive tetrapods may preclude their ability to increase speed.

A method for deriving displacement data during cyclical movement using an inertial sensor

Biomechanical studies often employ optical motion capture systems for the determination of the position of an object in a room-based coordinate system. This is not ideal for many types of study in locomotion since only a few strides may be collected per ;trial', and outdoor experiments are difficult with some systems. Here, we report and evaluate a novel approach that enables the user to determine linear displacements of a proprietary orientation sensor during cyclical movement. This makes experiments outside the constraints of the laboratory possible, for example to measure mechanical energy fluctuations of the centre of mass during over-ground locomotion. Commercial orientation sensors based on inertial sensing are small and lightweight and provide a theoretical framework for determining position from acceleration. In practice, the integration process is difficult to implement because of integration errors, integration constants and the necessity to determine the orientation of the measured accelerations. Here, by working within the constraints of cyclical movements, we report and evaluate a method for determining orientation and relative position using a modified version of a commercial inertial orientation sensor that combines accelerometers, gyroscopes and magnetometers, thus giving a full set of movement parameters (displacement, velocity and acceleration in three dimensions). The 35 g sensor was attached over the spine of a horse exercising on a treadmill. During canter locomotion (9.0 m s-1), the amplitudes of trunk movement in the x (craniocaudal), y (mediolateral) and z (dorsoventral) directions were 99.6, 57.9 and 140.2 mm, respectively. Comparing sensor displacement values with optical motion capture values for individual strides, the sensor had a median error (25th, 75th percentile) in the x, y and z directions of 0.1 (-9.7, +10.8), -3.8 (-15.5, +13.7) and -0.1 (-6.3, +7.1) mm, respectively. High-pass filtering of the displacement data effectively separated non-cyclical from cyclical components of the movement and reduced the interquartile ranges of the errors considerably to (-3.6, 6.2), (-4.0, 3.8) and (-4.5, 5.1) for x, y and z displacement, respectively, during canter locomotion. This corresponds to (-3.2, 5.5)%, (-6.7, 6.3)% and (-3.3, 3.7)% of the range of motion.

Analysis of slug tests in bypassed wells

In Berlin many wells are constructed with an additional small diameter bypass tube flanged on to the large diameter casing and running parallel to the later upward to the surface. The response to a slug test conducted in such a well is usually characterised by significant water level oscillations developing inside the branched pipe system. In the present paper, a general non-linear model is developed for the analysis of slug tests performed in bypassed wells. The model includes skin effects, non-linear head losses due to internal well bore fluid friction, minor losses originating at radius changes along the flow path inside the well, and inertial effects of the water columns contained within the primary casing and the bypass. Pipe flow inside the branched tubing system is described by the one-dimensional conservation law of the mechanical energy of the well bore fluid. Aquifer flow is quantified by a convolution-type approach. The coupled well-aquifer system is governed by an integro-differential equation representing the mean mechanical energy of the total well bore fluid and, coupled to it, by a non-linear ordinary differential equation which accounts for mechanical energy fluctuations between the water columns inside the main casing and the bypass. Both equations are solved by finite difference approximations coupled to point iterative numerical techniques. An application of the model to field data suggests that non-linear hydraulic head losses originating inside the well bore may cause the measured head responses to depend on the initial displacement. A packer used to initiate a slug test can induce these non-linear distortions through the combined effect of minor losses originating at the inlet and the outlet of a small diameter packer flow-through tube and internal fluid friction potentially developing inside that packer passage. As classical linear theories do not allow for the analysis of such phenomena, a model accounting for these non-linear processes should be used if field data show significant dependencies on the initial slug height.