A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

A comparison of the physiological demands of rugby union match-play when determined by absolute (ABS) or individual (IND) velocity bands in Global Positioning System (GPS) analysis

Since turning professional in 1995 there have been considerable advances in the research on the demands of rugby union, largely using Global Positioning System (GPS) analysis over the last 10 years. A systematic review on the use of GPS, particularly the setting of absolute (ABS) and individual (IND) velocity bands in field based, intermittent, high-intensity (HI) team sports was undertaken. From 3669 records identified, 38 studies were included for qualitative analysis. Little agreement on the definition of movement intensities within team sports was found, only three papers, all on rugby union, had used IND bands, with only one comparing ABS and IND methods. Thus, the aim of this study was to determine if there is a difference in the demands within positions when comparing ABS and IND methods for GPS analysis and if these differences are significantly different between the forward and back positional groups. A total of 214 data files were recorded from 26 players in 17 matches of the 2015/2016 Scottish BT Premiership. ABS velocity zones 1-7 were set at 1) 0-6, 2) 6.1-11, 3) 11.1-15, 4) 15.1-18, 5) 18.1-21, 6) 21.1-15 and 7) 25.1-40km.h-1 while IND zones 1-7 were 1) <20, 2) 20-40, 3) 40-50, 4) 50-70, 5) 70-80, 6) 80-95 and 7) 95-100% of player’s individually determined maximum velocity (Vmax). A 40m sprint test measured Vmax using OptaPro S4 10 Hz (catapult, Australia) GPS units to derive IND bands. The same GPS units were worn during matches. GPS outputs analysed were % distance, % time, high intensity efforts (HIEs) over 18.1 km.h-1 / 70% max velocity and repeated high intensity efforts (RHIEs) which consists of three HIEs in 21secs. General linear model (GLM) analysis identified a significant difference in the measurement of % total distance covered, between the ABS and IND methods in all zones for forwards (p<0.05) and backs (p<0.05). This difference was also significant between forwards and backs in zones 1, shown as mean difference ± standard deviation (3.7±0.7%), 6 (1.2±0.4%) and 7 (1.0±0.0%) respectively (p<0.05). Percentage time estimations were significantly different between ABS and IND analysis within forwards in zones 1 (1.7±1.7%), 2 (-2.9±1.3%), 3 (1.9±0.8%), 4 (-1.4±0.8%) and 5 (0.2±0.4%), and within backs in zones 1 (-10±1.5%), 2 (-1.2±1.1%), 3 (1.8±0.9%) and 5 (0.6±0.5%) (p<0.05). The difference between groups was significant in zones 1, 2, 4 and 5 (p<0.05). The number of HIEs was significantly different between forwards and backs in zones 6 (6±2) and 7 (3±2). RHIEs were significantly different between ABS and IND for forwards (1±2, p<0.05) although not between groups. Until more research on the differences in ABS and IND methods is carried out, then neither can be deemed a criterion method. In conclusion, there are significant differences between the ABS and IND methods of GPS analysis of the physical demands of rugby union, which must be considered when used to inform training load and recovery to improve performance and reduce injuries.