Eulerian-Lagrangian definition of coarse bed-load transport: Theory and verification with low-cost inertial measurement units

Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. This physical complexity has led to ambiguous definition of the reference frame (Lagrangian or Eulerian) in which sediment transport is analysed. A general Eulerian-Lagrangian approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. The necessary Eulerian-Lagrangian transformations are simplified under the assumption of an ideal Inertial Measurement Unit (IMU), rigidly attached at the centre of the mass of a sediment particle. Real, commercially available IMU sensors can provide high frequency data on accelerations and angular velocities (hence forces and energy) experienced by grains during entrainment and motion, if adequately customized. IMUs are subjected to significant error accu- mulation but they can be used for statistical parametrisation of an Eulerian-Lagrangian model, for coarse sediment particles and over the temporal scale of individual entrainment events. In this thesis an Eulerian-Lagrangian model is introduced and evaluated experimentally. Absolute inertial accelerations were recorded at a 4 Hz frequency from a spherical instrumented particle (111 mm diameter and 2383 kg/m3 density) in a series of entrainment threshold experiments on a fixed idealised bed. The grain-top inertial acceleration entrainment threshold was approximated at 44 and 51 mg for slopes 0.026 and 0.037 respectively. The saddle inertial acceleration entrainment threshold was at 32 and 25 mg for slopes 0.044 and 0.057 respectively. For the evaluation of the complete Eulerian-Lagrangian model two prototype sensors are presented: an idealised (spherical) with a diameter of 90 mm and an ellipsoidal with axes 100, 70 and 30 mm. Both are instrumented with a complete IMU, capable of sampling 3D inertial accelerations and 3D angular velocities at 50 Hz. After signal analysis, the results can be used to parametrize sediment movement but they do not contain positional information. The two sensors (spherical and ellipsoidal) were tested in a series of entrainment experiments, similar to the evaluation of the 111 mm prototype, for a slope of 0.02. The spherical sensor entrained at discharges of 24.8 ± 1.8 l/s while the same threshold for the ellipsoidal sensor was 45.2 ± 2.2 l/s. Kinetic energy calculations were used to quantify the particle-bed energy exchange under fluvial (discharge at 30 l/s) and non-fluvial conditions. All the experiments suggest that the effect of the inertial characteristics of coarse sediments on their motion is comparable to the effect hydrodynamic forces. The coupling of IMU sensors with advanced telemetric systems can lead to the tracking of Lagrangian particle trajectories, at a frequency and accuracy that will permit the testing of diffusion/dispersion models across the range of particle diameters.

Assessments of training load in elite youth soccer

One of the most popular sports globally, soccer has seen a rise in the demands of the game over recent years. An increase in intensity and playing demands, coupled with growing social and economic pressures on soccer players means that optimal preparation is of paramount importance. Recent research has found the modern game, depending on positional role, to consist of approximately 60% more sprint distance in the English Premier League, which was also found to be the case for frequency and success of discrete technical actions (Bush et al., 2015). As a result, the focus on soccer training and player preparedness is becoming more prevalent in scientific research. By designing the appropriate training load, and thus periodization strategies, the aim is to achieve peak fitness in the most efficient way, whilst minimising the risk of injury and illness. Traditionally, training intensity has been based on heart rate responses, however, the emergence of tracking microtechnology such as global positioning system (GPS) and inertial sensors are now able to further quantify biomechanical load as well as physiological stress. Detailed pictures of internal and external loading indices such as these then combine to produce a more holistic view of training load experience by the player during typical drills and phases of training in soccer. The premise of this research is to gain greater understanding of the physical demands of common training methodologies in elite soccer to support optimal match performance. The coaching process may then benefit from being able to prescribe the most effective training to support these. The first experimental chapter in this thesis began by quantify gross training loads of the pre-season and in-season phases in soccer. A broader picture of the training loads inherent in these distinct phases brought more detail as to the type and extent of external loading experienced by soccer players at these times, and how the inclusion of match play influences weekly training rhythms. Training volume (total distance) was found to be high at the start compared to the end of pre-season (37 kilometres and 28 kilometres), where high cardiovascular loads were attained as part of the conditioning focus. This progressed transiently, however, to involve higher-speed, acceleration and change-of-direction stimuli at the end of pre-season compared to the start and to that in-season (1.18 kilometres, 0.70 kilometres and 0.42 kilometres high-intensity running; with 37, 25 and 23 accelerations >3m/s2 respectively) . The decrease in volume and increase in maximal anaerobic activity was evident in the training focus as friendly matches were introduced before the competitive season. The influence of match-play as being a large physical dose in the training week may then determine the change in weekly periodisation and how resulting training loads applied and tapered, if necessary. The focus of research was then directed more specifically to the most common mode of training in soccer, that also featured regularly in the pre-season period in the present study, small-sided games (SSG). The subsequent studies examined numerous manipulations of this specific form of soccer conditioning, such as player numbers as well as absolute and relative playing space available. In contrast to some previous literature, changing the number of players did not seem to influence training responses significantly, although playing format in the possession style brought about larger effects for heart rate (89.9%HRmax) and average velocity (7.6km/h-1). However, the following studies (Chapters 5, 6 and 7) revealed a greater influence of relative playing space available to players in SSG. The larger area at their disposal brought about greater aerobic responses (~90%HRmax), by allowing higher average and peak velocities (>25km/h-1), as well as greater distance acceleration behaviour at greater thresholds (>2.8m/s2). Furthermore, the data points towards space as being a large determinant in strategy of the player in small-sided games (SSG), subsequently shaping their movement behaviour and resulting physical responses. For example, higher average velocities in a possession format (8km/h-1) reflects higher work rate and heart rate load but makes achieving significant neuromuscular accelerations at a high level difficult given higher starting velocities prior to the most intense accelerations (4.2km/h-1). By altering space available and even through intentional numerical imbalances in team numbers, it may be easier for coaches to achieve the desired stimulus for the session or individual player, whether that is for aerobic and neuromuscular conditioning. Large effects were found for heart rate being higher in the underloaded team (85-90%HRmax) compared to the team with more players (80-85%HRmax) as well as for RPE (5AU versus 7AU). This was also apparent for meterage and therefore average velocity. It would also seem neuromuscular load through high acceleration and deceleration efforts were more pronounced with less numbers (given the need to press and close down opponents, and in a larger area relative to the number of players on the underloaded team. The peak accelerations and deceleration achieved was also higher when playing with less players (3-6.2m/s2 and 3-6.1m/s2) Having detailed ways in which to reach desired physical loading responses in common small training formats, Chapter 8 compared SSG to larger 9v9 formats with full-size 11v11 friendly matches. This enabled absolute and relative comparisons to be made and to understand the extent to which smaller training formats are able to replicate the required movements to be successful in competition. In relative terms, it was revealed that relative acceleration distance and Player Load were higher in smaller 4v4 games than match-play (1.1m.min-1 and 0.3m.min-1 >3m/s2; 16.9AU versus 12AU). Although the smallest format did not replicate the high-velocity demands of matches, the results confirmed their efficacy in providing significant neuromuscular load during the training week, which may then be supplemented by high-intensity interval running in order to gain exposure to more maximal speed work. In summary, the data presented provide valuable information from GPS and inertial sensor microtechnology which may then be used to understand training better to manipulate types of load according to physical conditioning objectives. For example, a library of resources to direct planning of drills of varying cardiovascular, neuromuscular and perceptual load can be created to give more confidence in session outcomes. Combining external and internal load data of common soccer training drills, and their application across different phases and training objectives may give coaches a powerful tool to plan and periodize training.