Dynamic similarity during human running: About Froude and Strouhal dimensionless numbers

The Measure of Motion Similarity for Robotics Application

A new measure of motion similarity has been proposed. The formulation of this measure is presented and its logical basis is described. Unlike in most of other methods, the measure enables easy determination of the instantaneous synergies of the motion of body parts. To demonstrate how to use the measure, the data describing human movement is used. The movement is recorded using a professional motion capture system. Two different cases of non-periodic movements are discussed: stepping forward and backward, and returning to a stable posture after an unexpected thrust to the side (hands free or tied). This choice enables the identification of synergies in slow dynamics (stepping) and in fast dynamics (push recovery). The trajectories of motion similarity measures are obtained for point masses of the human body. The interpretation of these trajectories in relation to motion events is discussed. In addition, ordinary motion trajectories and footprints are shown in order to better illustrate the specificity of the discussed examples. The article ends with a discussion and conclusions.

Effects of Shoe Midfoot Bending Stiffness on Multi-Segment Foot Kinematics and Ground Reaction Force during Heel-Toe Running

We investigated how midfoot stiffness of running shoes influences foot segment kinematics and ground reaction force (GRF) during heel-toe running. Nineteen male rearfoot strike runners performed overground heel-toe running at 3.3 m/s when wearing shoes with different midfoot bending stiffnesses (low, medium, and high) in a randomized order. A synchronized motion capture system (200 Hz) and force plate (1000 Hz) were used to collect the foot-marker trajectories and GRF data. Foot kinematics, including rearfoot-lab, midfoot-rearfoot, forefoot-rearfoot, and forefoot-midfoot interactions, and kinetics, including GRF characteristics, were analyzed. Our results indicated that high midfoot stiffness shoes reduced the forefoot-rearfoot range of motion (mean ± SD; high stiffness, 7.8 ± 2.0°, low stiffness, 8.7 ± 2.1°; p < 0.05) and forefoot-midfoot range of motion (mean ± SD; high stiffness, 4.2 ± 1.1°, medium stiffness, 4.6 ± 0.9°; p < 0.05) in the frontal plane. No differences were found in the GRF characteristics among the shoe conditions. These findings suggest that an increase in midsole stiffness only in the midfoot region can reduce intersegmental foot medial-lateral movements during the stance phase of running. This may further decrease the tension of the foot muscles and tendons during prolonged exercises.

Characteristics and main factors of foam flow in broken rock mass in coal mine goaf

To protect the environment and reduce the occurrence of coal mine fire, foam injection in goafs is an effective measure for preventing and extinguishing mine fires. The flow characteristics of foams injected into goafs have a significant impact on the prevention and extinguishment of such fires. To study the flow characteristics of foam injected into a goaf, we first independently constructed a set of experimental platforms for the visualization of goafs. Next, we performed physical experiments on foam injection using similarity theory. Flow characteristics were simulated under different foam concentrations, flow rates, and goaf porosities. The exponential function was found to provide a good fit to the trajectory of the foam's stacking edge in the goaf. According to the foam injection volume, the trend of the fitting equation parameter a could be divided into two stages. The first stage was the rapidly decreasing stage, and the second stage was the stable stage. It was inferred that the stacking height and diffusion radius of the foam under different conditions were related to the speed of liquid film drainage. The results of this study can provide a valuable reference for the use of fire prevention and extinguishment technology in the goaf.

Evaluating dynamic similarity of fixed, self-selected and anatomically scaled speeds in non-linear analysis of gait during treadmill running

OBJECTIVES

The aim of this study is to evaluate how speed affects non-linear measures of variability. Fixed and self-selected speeds were compared to an anatomically scaled speed calculated based on leg length to evaluate which provided a more reproducible result between subjects.

METHODS

Sixteen subjects ran on a treadmill at a fixed, scaled and self-selected speed and at ±10% in each case. Kinematic data were collected for two minutes at 250 Hz for each trial. Sample entropy (SaEn) and maximum Lyapunov exponents (LyE) were calculated from the sagittal knee and hip joint angles to evaluate regularity of gait and local stability. These nonlinear measures were compared to evaluate the dynamic similarity of the movement in each case, and to evaluate speed as a confounding variable in non-linear analysis.

RESULTS

An anatomically scaled speed shows more dynamic similarity than a fixed or self-selected speed with the lowest observed coefficient of variation for each measure. This was found to be statistically significant for both nonlinear measures of the hip (SaEn p = 0.038; LyE p = 0.040). Speed was not found to be a confounding variable in non-linear analysis of running gait of a healthy population (η² < 0.05).

CONCLUSIONS

Changes in speed by ±10% do not significantly affect stability and variability of gait for healthy participants, suggesting that they make adaptations to ensure optimal gait variability. Anatomically scaled speeds provide a more reliable methodology for both linear and non-linear analysis by providing a definitive protocol, suggesting it could replace self-selected or fixed speeds in future research.

On the mechanical power output required for human running - Insight from an analytical model

In this paper the dynamics of human running on flat terrain and the required mechanical power output with its dependency on various parameters is investigated. Knowing the required mechanical power output is of relevance due to its relationship with the metabolic power. For example, a better understanding of the dependencies of required mechanical power output on weight, running and wind speed, step frequency, ground contact time etc. is very valuable for the assessment, analysis and optimization of running performance. Therefore, a mathematical model based on very few assumptions is devised. The purpose of the proposed model is to relate running speed and required mechanical power output as an algebraic function of the runner's mass, height, step rate, ground contact time and wind speed. This is relevant in order to better understand the mechanical energy cost of locomotion, and how much it depends on which parameters. The first of the main energy dissipation mechanisms is due to vertical oscillation, i.e., during each step some of the potential energy difference gets transformed into heat. The second mechanism is due to the anterior ground reaction force during the first part of stance and the third is due to aerodynamic drag. With the approximations of constant running speed and a sinusoidal vertical ground reaction force profile one obtains closed algebraic expressions for the center of mass trajectory and the required mechanical power output. Comparisons of model predictions and reported performance data suggest that approximately a quarter of the ground impact energy is stored during the first part of ground contact and then released during the remaining stance phase. Further, one can conclude from the model that less mechanical power output is required when running with higher step rates and a higher center of mass. Non intuitive is the result that a shorter ground contact time is beneficial for fast runs, while the opposite holds for slow runs. An important advantage of the devised model compared to others is that it leads to closed algebraic expressions for the center of mass trajectory and mechanical power output, which are functions of measurable quantities, i.e., of step rate, ground contact time, running speed, runner's mass, center of mass height, aerodynamic drag at some given speed, wind speed and heart rate. Moreover, the model relies on very few assumptions, which have been verified, and the only tuning parameter is the ratio of recovered elastic energy.

Walking dynamic similarity induced by a combination of Froude and Strouhal dimensionless numbers: Modela-w

The aim of this study was to assess the accuracy of a new dimensionless number associating Froude (Nfr) and Strouhal (Str) called Modela-w to induce walking dynamic similarity among humans of different sizes. Nineteen subjects walked in three experimental conditions: (i) constant speed, (ii) similar speed (Nfr) and (iii) similar speed and similar step frequency (Modela-w). The dynamic similarity was evaluated from scale factors computed with anthropometric, temporal, kinematic and kinetic data and from the decrease of the variability of the parameters expressed in their dimensionless form. Over a total of 36 dynamic parameters, dynamic similarity from scale factors was met for 11 (mean r = 0.51), 22 (mean r = 0.52) and 30 (mean r = 0.69) parameters in the first, the second and the third experimental conditions, respectively. Modela-w also reduced the variability of the dimensionless preceding parameters compared to the other experimental conditions. This study shows that the combination of Nfr and Str called Modela-w ensures dynamic similarity between different-sized subjects and allows scientists to impose similar experimental conditions removing all anthropometric effects.

Normalization of ground reaction forces, joint moments, and free moments in human locomotion

Authors who report ground reaction force (GRF), free moment (FM), and resultant joint moments usually normalize these variables by division normalization. Normalization parameters include body weight (BW), body weight x height (BWH), and body weight x leg length (BWL). The purpose of this study was to explore the appropriateness of division normalization, power curve normalization, and offset normalization on peak GRF, FM, and resultant joint moments. Kinematic and kinetic data were collected on 98 subjects who walked at 1.2 and 1.8 m/s and ran at 3.4 and 4.0 m/s. Linear curves were best fit to the data, and regression analyses performed to test the significance of the correlations. It was found that the relationship between peak force and BW, as well as joint moments and BW, BWH, and BWL, were not always linear. After division normalization, significant correlations were still found. Power curve and offset normalization, however, were effective at normalizing all variables; therefore, when attempting to normalize GRF and joint moments, perhaps nonlinear or offset methods should be implemented.

Thermoregulation and endurance running in extinct hominins: Wheeler's models revisited

Thermoregulation is often cited as a potentially important influence on the evolution of hominins, thanks to a highly influential series of papers in the Journal of Human Evolution in the 1980s and 1990s by Peter Wheeler. These papers developed quantitative modeling of heat balance between different potential hominins and their environment. Here, we return to these models, update them in line with new developments and measurements in animal thermal biology, and modify them to represent a running hominin rather than the stationary form considered previously. In particular, we use our modified Wheeler model to investigate thermoregulatory aspects of the evolution of endurance running ability. Our model suggests that for endurance running to be possible, a hominin would need locomotive efficiency, sweating rates, and areas of hairless skin similar to modern humans. We argue that these restrictions suggest that endurance running may have been possible (from a thermoregulatory viewpoint) for Homo erectus, but is unlikely for any earlier hominins.