Changes in Energy Cost and Total External Work of Muscles in Elite Race Walkers Walking at Different Speeds

The aim of the study was to assess the influence of year-long training of race walkers on physiological cost and total energy center of mass (CoM). The assessment performed was based on indicating the differences between the resulting energy cost in a group of elite race walkers walking at technical, threshold, and racing speeds calculated by physiological and biomechanical methods before beginning and after finishing a year-long training cycle. The study involved 12 competitive race walkers who had achieved champion or international champion level. Their aerobic endurance was determined by means of a direct method, applying an incremental exercise test on the treadmill. The gait of the participants was recorded using the 3D Vicon analysis system. Changes in mechanical energy amounted to the value of the total external work of the muscles needed to accelerate and lift the center of mass during a normalized gait cycle. The highest influence on the total external work increase for increasing speeds of gait in both examinations was attributed to the changes in the kinetic energy resulting from the center of mass movement. A statistically significant decrease of the mean value of total external work for racing speed was observed in the second examination (p < 0.001). An approx. 8% decrease (NS) of EE energy cost, standardized by body mass and distance covered, was found between the first and second examinations. The energy cost and total external work were significantly differentiated by the walkers’ gait speeds (p < 0.05–0.001). The energy cost significantly differed from the total external work at p < 0.001.

Despite equivalent changes in potential energy, work calculated from joint powers during stair descent was lower than work during stair ascent (1). We now hypothesize the generalized biomechanical principle that lower extremity muscles dissipate less mechanical energy during gait tasks that lower the body center of mass compared to the energy they generate during gait tasks that raise the center of mass. PURPOSE The purpose of this study was to compare work produced by lower extremity muscles in healthy young and old adults while walking up and down a surface inclined 10°. METHODS 20 young and 10 old adults (mean ages 76 & 22 yr) were videotaped walking at 1.5 m/s up and down a ramp over a force plate. Lower extremity joint powers and work were calculated through inverse dynamics. This work quantifed muscle contributions to changes in energy. Total work per step was calculated from the change in potential energy per step in ramp ascent and descent. RESULTS Mean step length was 4% larger in ascent vs descent (0.63 vs 0.60 m, t-test, p<.05) as was the change in potential energy. Joint work however was 31% higher in ascent vs descent (68 vs. 51 J/step, p<.001). Ascent joint work was statistically identical to the total work done to raise the subjects' masses through the observed vertical displacement (68 vs 70 J/step, p<.05) while descent joint work was 24% lower than the total work done to lower the subjects' masses (51 v 67 J/step, p<.001). Young and old subjects were statistically identical. CONCLUSIONS Lower extremity muscles produced more work in ascending vs descending an inclined surface despite similar changes in total potential energy. This result was observed in two populations with different gait mechanics. Work from other tissues in the lower extremity or other body segments during descent most likely accounted for this discrepancy. (1) DeVita et al. Neuromuscular reorganization during stairway locomotion in old adults ACSM Conference, Baltimore, Maryland, 2001.

This study presents a novel approach to calculating the average change in kinetic energy of galaxies exhibiting non-relativistic motion. The methodology integrates the dynamics of total observed motion, which encompasses both peculiar and recessive motion, with the gravitational influence of neighboring galaxies. The peculiar motion is quantified through peculiar redshift, while recessive motion is described by Hubble’s Law. The total observed velocity is the sum of these two components. The research derives an expression for the average acceleration of a galaxy based on the change in its total observed redshift wavelength over time. Utilizing Newton’s Second Law of Motion, the average observed force and subsequent work done by this force is calculated. The work done by conservative forces, primarily gravitational forces exerted by neighboring galaxies, is also considered to determine the total work done on the galaxy. Results indicate that the average total observed force causing the motion of a galaxy is a non-conservative force, resulting from the combined effects of non-conservative forces responsible for peculiar and recessive motion. The change in potential energy due to gravitational interactions with neighboring galaxies is accounted for, leading to the formulation of the average change in kinetic energy. The conclusion of the paper provides a comprehensive expression for the average change in kinetic energy of a galaxy, factoring in the mass of the galaxy, the speed of light, the total observed redshift, the change in distance with respect to Earth, and the gravitational constant. This expression is significant for understanding the dynamics of galactic motion and the forces at play in a non-relativistic context.

Conservation of total, kinetic, and thermal energy in the atmosphere is revisited, and the derived thermal energy balance is examined with observations. Total energy conservation (TEC) provides a constraint for the sum of kinetic, thermal, and potential energy changes. In response to air thermal expansion/compression, air density variation leads to vertical density fluxes and potential energy changes, which in turn impact the thermal energy balance as well as the kinetic energy balance due to the constraint of TEC. As vertical density fluxes can propagate through a large vertical domain to where local thermal expansion/compression becomes negligibly small, interactions between kinetic and thermal energy changes in determining atmospheric motions and thermodynamic structures can occur when local diabatic heating/cooling becomes small. The contribution of vertical density fluxes to the kinetic energy balance is sometimes considered but that to the thermal energy balance is traditionally missed. Misinterpretation between air thermal expansion/compression and incompressibility for air volume changes with pressure under a constant temperature would lead to overlooking important impacts of thermal expansion/compression on air motions and atmospheric thermodynamics. Atmospheric boundary layer observations qualitatively confirm the contribution of potential energy changes associated with vertical density fluxes in the thermal energy balance for explaining temporal variations of air temperature.

This study aimed to elucidate how external mechanical work done during maximal acceleration sprint running changes with increasing running velocity and is associated with running performance. In twelve young males, work done at each step over 50 m from the start was calculated from mechanical energy changes in horizontal anterior-posterior and vertical directions and was divided into braking (-W kap and - W v, respectively) and propulsive (+ W kap and + W v, respectively) phases. The maximal running velocity (V max) appeared at 35.87±7.76 m and the time required to run 50 m (T 50 m) was 7.11±0.54 s. At 80% V max or higher, +W kap largely decreased and -W kap abruptly increased. The change in the difference between +W kap and |-W kap| (ΔW kap) at every step was relatively small at 70% V max or lower. Total work done over 50 m was 82.4±7.5 J kg-1 for +W kap, 36.2±4.4 J kg-1 for |-W kap|, 14.3±1.9 J kg-1 for +W v, and 10.4±1.2 J kg-1 for |-W v|. The total ΔW kap over 50 m was more strongly correlated with T 50 m (r=-0.946, P<0.0001) than the corresponding associations for the other work variables. These results indicate that in maximal sprint running over 50 m, work done during the propulsive phase in the horizontal anterior-posterior direction accounts for the majority of the total external work done during the acceleration stage, and maximizing it while suppressing work done during the braking phase is essential to achieve a high running performance.

One of the key features that enables animals and humans to perform agile, robust, adaptive yet ef- ficient locomotion is their body’s complex muscle-tendon-ligament system. Such systems provide body and limbs with the functionality that is used to efficiently absorb external shocks and ex- change of mechanical energy, e.g. kinetic and potential energy, to exploit natural dynamics during locomotion. In biology, it has been found that animals and humans adjust their limb stiffness to ac- commodate for different speeds, gaits, and terrains. On contrary, in the field of legged robots, little has been known about how to control leg stiffness to efficiently adapt to changes of speed, terrain, and gait or stride frequency at which the leg oscillates. Therefore, this thesis aims at contributing to the primary understanding of the topic. Until today, mechanical springs with fixed spring constants are still widely used as energy sav- ing mechanisms and shock absorbers for legged robots. However, the compliance of those springs is not adjustable and manual assembly is required to make a robot leg stiffer or more compliant. Motivated by this fact, we present a systematic development and evaluation of a new variable compliance/stiffness actuator, named MESTRAN (MEchanism to vary Stiffness via Transmission ANgle) in this thesis. This actuator serves as a key tool to investigate energy efficient locomotion at various stride frequencies and on surfaces with different stiffness. MESTRAN can dynamically alter joint stiffness in an unlimited range. It is also capable of maintaining the stiffness without requiring energy and offering different types of compliance, e.g. linear, quadratic, or exponential. In this thesis, we first designed and constructed an adjustable stiffness leg based on the MES- TRAN design. We then validated the design by conducting a series of experiments by using the first leg prototype. Second, in order to investigate hopping locomotion with variable stiffness ca- pability, we designed a single-legged robot, named L-MESTRAN (Linear-MESTRAN), which is an advanced version of the MESTRAN leg. We systematically analysed and demonstrated the me- chanical performance of the legged robot using the simulations and a number of real-world hop- ping experiments. As a result, we found that a proper adjustment of leg stiffness can improve the hopping energy efficiency of the robot at various stride frequencies. Third, this finding was also investigated on surfaces with different stiffness by using the L-MESTRAN robot. The simulation and experimental results indicated that, for a particular stride frequency (3 - 6 [Hz]), the adjust- ment of the knee stiffness can accommodate for changes in surface compliance, resulting in an improvement of the energy efficiency of hopping

James Rabchuk's recent paper1 describes a method for measuring the kinetic energy changes in the Gauss accelerator, as well as a calculation of the change in potential energy. In this paper, a simple method for measuring both the change in potential energy and the change in kinetic energy will be presented. The measurements can be made with rulers, strings, and weights. In the process, your students will learn about the relationship between work and potential energy as well as the law of conservation of energy. Issues associated with the law of conservation of momentum in the accelerator will also be addressed.

In section 1–2 a certain space-smoothing operation is defined and its usefulness in solving elliptic equations is demonstrated in the case of a Poisson equation. It leads to solutions in a closed form which possess the numerical simplicity of the ordinary iteration methods, but is converging more rapidly. The reverse operation of unsmoothing is also defined as far as it can be done, and it is mentioned that the combined processes of smoothing and unsmoothing are convenient tools for obtaining a spectral analysis of horizontal scalar fields, and also to remove systematical errors which are made when derivatives are taken as finite differences.&#x0D; In sections 3–6 the application of smoothing is shown in the barotropic forecasting problem. At first a general theorem is proved concerning trajectories of two-dimensional non-divergent flow. It states that if the streamfunction ψ1 of such a flow can be decomposed into two components ψ2, α of which α is individually conserved in the ψ1-motion, then the displacements of the fluid particles up to any time can be found by at first displacing in the stationary flow αt=0 = const and then adding from the resulting positions the displacements in the flow with the streamfunction ψ2. The theorem is first applied to barotropic flow. In this case the first stationary field to displace in is the deviation between the actual and smoothed flow, while the second field to displace in is the smoothed flow.&#x0D; The space-smoothing is next applied to an equation expressing the individual conservation of a quantity s in a two-dimensional non-divergent flow. The Reynolds term belonging to the smoothed equation is studied and found to depend essentially upon the deformation properties of the velocity field. The role of deformation for the net spectral flow of energy in the s-field is studied. The smoothing is in particular applied to the vorticity equation to show how this possibly can be utilized in the integration problem.&#x0D; In sections 7–11 the baroclinic case is considered. In sections 7–8 is shown the fundamental role of deformation for the interchange of potential and kinetic energy. It is found that in the advective model there is direct proportionality between the change in total kinetic energy and total thermal wind energy, and also a direct proportionality between the change in kinetic energy for the vertically mean motion and the thermal wind energy.&#x0D; In section 9 is discussed the possible importance of non-linear interference for the understanding of the creation and local distribution of disturbances in the atmosphere.&#x0D; The integration problem is discussed in sections 10–12. At first an extension of the barotropic displacement rule is given for the vertically mean motion. The trajectory problem for levels other than the mean level is touched in section 12, and a simple non-advective model discussed shortly in section 11.

A one-dimensional model of upper-ocean vertical mixing is used to investigate the ocean's response to idealized atmospheric storms over short (1–2 day) timescales. Initial ocean conditions are based on observations from the northeast Pacific. When the wind rotation is resonant at the inertial frequency, the surface input of kinetic energy to the currents, KE0, is maximized, as are the net changes in inertial kinetic energy, potential energy, and sea surface temperature. The KE0 is a key air–sea interaction parameter because of its strong dependence on the time histories of the wind forcing and surface current, and because some of this kinetic energy input can go to increasing potential energy when dissipated in regions of large buoyancy gradients below the mixed layer. Energy input and the ocean response are rapidly reduced for less inertial winds, indicating that the upper ocean has highly tuned inertial resonant responses. The degree of tuning is highest for the inertial kinetic energy response, followed by KE0 input, the potential energy, and temperature responses. For storms of varying strength, duration, shape, and wind rotation, about 20% of the final inertial current energy is found beneath the mixed layer, regardless of the stratification. The magnitude of inertial current response depends on KE0 and wind rotation, but not stratification, and is approximately 0.532 KE0[1–e−2.81], where Γ is a function of wind rotation that varies from 1 for purely inertial winds to 0 for winds with no energy at the inertial frequency. Changes in potential energy and surface temperature depend mainly on KE0 and stratification, but not systematically on wind rotation other than as accounted for in KE0. Initial currents can modulate KE0 and the responses significantly; the modulation varies roughly linearly with initial current speed, consistent with a simple scale analysis. Modulation of each measure of ocean response is similar, so that there is little effect on general relationships formed by normalizing the responses with KE0, except for certain special phase relationships between the initial current direction and wind direction. Parameterizations of KE0 and of the mechanical production of turbulent kinetic energy should include both wind speed (or friction velocity) and rotation of the wind.

“The total work done by the external forces acting on a rigid body is equal to the change in the kinetic energy of the body.” O.K. ? Well, it all depends on definitions. The work done by a constant force is usually (in nearly all textbooks ?) defined as the product of the magnitude of the force and the displacement of its point of application, this displacement being measured in the direction of the force. Consider then a sheet of paper on which a student has drawn in pencil a straight line which he is now about to erase. He causes the eraser as it moves along to exert a constant force on it, and he exerts another constant force with his other hand to keep the paper still. The desk (supposed smooth) exerts constant normal forces. Of all these forces on the paper the first force does some work, according to the definition, while the others do none. The total work done by them is positive, yet there is no change in kinetic energy of the paper.

Right Ventricular–Pulmonary Vascular Interactions: An Emerging Role for Pulmonary Artery Acceleration Time by Echocardiography in Adults and Children

The general energy equation, including change in kinetic energy, was solved by numerical integration and used to evaluate simplifying assumptions and application practices over a wide range of conditions. When extreme conditions were encountered, sizable errors were caused by large integration intervals, application of Simpson's rule and neglecting change in kinetic energy. A maximum error of only 1.31 percent was caused by assuming temperature and compressibility constants at their average value. It was discovered that a discontinuity can develop in the integral for the injection cave. This discontinuity indicates a point of zero pressure change and is an inflection point in the pressure traverse. Introduction When a pressure in a gas well is to be calculated, one of the first decisions is to select a method of calculation. In many instances, this selection becomes a problem because the literature, at best, provides an evaluation of any method for only a limited range of conditions. Once a method has been selected, a question often arises as to the size of the calculation interval which should be used. The question regarding calculation interval arises because an analytic solution is not obtainable and approximate solutions must be used. This paper presents an evaluation of major assumptions and application practices of probably the two most widely used methods for calculating steady-state single-phase gas well pressure. The two methods are Cullender and Smith (numerical integration), and average temperature and compressibility. The Cullender-Smith method assumes that change in kinetic energy is negligible and is normally applied in two steps with a Simpson's rule correction. The average temperature and compressibility method, in addition to neglecting kinetic energy change, assumes that temperature and compressibility are constant at their average values. This method is normally applied for wellhead shut-in pressures of less than 2,000 psi, and in one step. Computer programs were written to compute bottom-hole pressure with and without the assumptions, using various approaches. Values of input parameters investigated are shown in Table 1. Flow rate was limited to a maximum of 5,000 and 10,000 Mcf/D for tubing sizes of 1.610 and 1.995 in. ID, respectively. Flow rate was also limited to 10,000 Mcf/D for a tubing size of 2.441 in. ID when wellhead flowing pressure was 100 psia. These limitations were imposed on flow rate so as not to exceed sonic velocity. The z factor routine available necessitated limiting bottom-hole temperature to 240F and wellhead pressure to 3,000 psia. Pressures were compared on the basis of percent deviation from the trapezoidal integration of Eq. 1 or 2 at 100-ft intervals. A preliminary investigation indicated that a 1,000-ft interval solution would differ from a 50-ft interval solution by less than 0.25 percent; therefore, the 100-ft interval was chosen for a base. For the purpose of comparison, deviations less than 1 percent were considered insignificant. EQUATIONS Cullender and Smith give the equation for calculating pressure in a dry gas well, neglecting kinetic energy change, as .........(1) if change in kinetic energy is considered, Eq. 1 becomes ,..........(2) where 111.1 q /d(4)p = kinetic energy term. Eqs. 1 and 2 can be evaluated numerically at specific depths using the trapezoidal rule as shown by Cullender and Smith. If change in kinetic energy is neglected and temperature and compressibility are assumed constant at their average values, Eq. 1 can be integrated to give the average temperature and compressibility equation, ,....(3)

In this paper, we provide a smooth extension of the energy aware Gauss‐Seidel iteration to the Position‐Based Dynamics (PBD) method. This extension is inspired by the kinetic and potential energy changes equalization and uses the foundations of the recent extended version of PBD algorithm (XPBD). The proposed method is not meant to conserve the total energy of the system and modifies each position constraint based on the equality of the kinetic and potential energy changes within the Gauss‐Seidel process of the XPBD algorithm. Our extension provides an implicit solution for relatively better stiffness during the simulation of elastic objects. We apply our solution directly within each Gauss‐Seidel iteration and it is independent of both simulation step‐size and integration methods. To demonstrate the benefits of our proposed extension with higher frame rates, we develop an efficient and practical mesh coloring algorithm for the XPBD method which provides parallel processing on a GPU. During the initialization phase, all mesh primitives are grouped according to their connectivity. Afterwards, all these groups are computed simultaneously on a GPU during the simulation phase. We demonstrate the benefits of our method with many spring potential and strain‐based continuous material constraints. Our proposed algorithm is easy to implement and seamlessly fits into the existing position‐based frameworks.

In mines where the natural caving method is used, the frequent occurrence of underground debris flows and the complex mine environments make it difficult to prevent and control underground debris flows. The source is one of the critical conditions for the formation of debris flows, and studying the impact of source material gradation on underground debris-flow disasters can effectively help prevent and control these occurrences. This paper describes a multiscale study of underground debris flows using physical model experiments and the discrete-element method (PFC3D) to understand the impact of the source material gradation on the disaster mechanism of underground debris flows from macroscopic and microscopic perspectives. Macroscopically, an increase in content of medium and large particles in the gradation will enhance the instantaneous destructive force. Large particles can more easily cause disasters than medium and fine particles with the same content, but the disaster-causing ability is minimized when the contents of medium and large particles exceed 50% and 60%, respectively. With increasing fine particle content, the long-distance disaster-causing ability and duration is increased. On the microscopic level, the source-level pairs affect the initial flow mode, concentration area of the force chain, average velocity, average runout distance, and change in energy of the underground debris flow. Among them, the proportion of large particles in the gradation significantly affects the change in kinetic energy, change in dissipative energy, time to reach the peak kinetic energy, and time of coincidence of dissipative energy and gravitational potential energy. The process of underground debris flow can be divided into a “sudden stage”, a “continuous impact stage”, and a “convergence and accumulation stage”. This work reveals the close relationship between source material gradation and the disaster mechanism of underground debris flows and highlights the necessity of considering the source material gradation in the prevention and control of underground debris flows. It can provide an important basic theory for the study of environmental and urban sustainable development.

This study employed a low-cost method for quantifying bouncing ball dynamics with smartphone video. High-speed video analysis was used to investigate the bouncing behaviour of different balls, including table tennis, rubber, and tennis balls, on a table tennis surface. To examine the effect of surface material on bouncing dynamics, the table tennis ball was also tested on wood and tile surfaces. Key parameters analysed included bounce height decay, the coefficient of restitution (COR), and the bounce half-life. Additionally, we measured the total bouncing time and analysed the relationship between changes in gravitational potential energy, kinetic energy, and total mechanical energy (ME). Our results revealed a significant correlation between the COR and the decay rate of bounce height. Balls with higher COR values, indicative of lower energy loss per bounce, exhibited slower decay rates, resulting in longer bounce half-lives and extended total bounce times. For instance, the table tennis ball on a tile surface demonstrated a high COR of 0.93, a bounce half-life of 4.65 bounces, and a total bounce time of 8.22 ± 0.34 s. This suggests that material properties such as stiffness and elasticity of both the ball and the surface significantly influence the COR and decay rate, beyond just surface smoothness. Furthermore, our analysis of ME changes in the bouncing balls aligns with theoretical predictions, providing insights into the energy transformations occurring during bouncing. This improved understanding can also be a valuable tool for educators, helping teachers and students bridge the gap between theory and real-world observations, leading to a deeper grasp of the concepts.