The research presented in this thesis aims to improve the knowledge of head impact biomechanics in youth football players by analyzing head impact exposure of youth football players and the performance of youth football helmets. The results of the studies presented provide a foundation for researchers, football leagues, and helmet manufactures to implement changes and modifications that aim to reduce concussion risk in youth athletes. The first study presented in this thesis aims to quantify the head impact exposure of 7 to 8 year old football players and determine the cause of variation in player exposure. To conduct this study, 19 players were instrumented with helmet mounted accelerometers that measured real-time acceleration data on the field. This data was analyzed to determine the magnitude, frequency, and location of each impact sustained by players in the 2011 and 2012 football season. From these data, it was determined that the average 7 to 8 year old player experienced 161 impacts per season, 60% of which were in practice and 40% were in games. The median impact for 7 to 8 year old players was 16 g and 686 rad/s². The magnitude of the 95th percentile impact was 38 g and 2052 rad/s². A total of 125 impacts above 40 g were recorded, 67% of which occurred in practices and 33% occurred in games. It was determined that returning players experienced significantly more impacts per season than first time players and practices had significantly higher magnitude impacts than games. These data can be used to further develop practice modifications that aim to reduce total impacts and high magnitude impacts experienced by youth football players. The second study presented in this thesis aims to quantify differences in youth football helmet performance before and after a football season. Currently, the only requirement regarding helmet recertification and reconditioning states that no helmet older than 10 years will be recertified or reconditioned. Quantitative data is needed to either support or refute this guideline and provide data describing how often youth football helmets should be recertified and reconditioned. To conduct this study, 6 youth Riddell Revolution football helmets, 3 that were new and 3 that had been used for one season, were tested on a drop tower from various heights and impact locations before and after the 2013 football season. It was determined that there was no significant difference in helmet performance before and after a season for new helmets or helmets that had been used for one season. In addition, there was no significant correlation between the frequency of impacts, the 95th percentile impact magnitude, or the product of the frequency and 95th percentile impact magnitude with the change in helmet performance. Future studies should be conducted that analyze the performance of youth football helmets over the course of multiple seasons. / Master of Science

When football originated in the 1800s, players wore no protective equipment. Between 1869 and 1905, there were 18 deaths and 159 serious injuries attributed to the sport. Following this, players began to wear protective equipment. The first use of a football helmet was in 1893, made of leather and designed to reduce the risk of skull fracture. Initially, football helmets were intended to protect a player against the most severe hits they would experience on the field. More recently, it has been shown that mild traumatic brain injuries, such as concussions, can induce long-term neurodegenerative processes. Since their introduction, helmets have transformed into plastic shells with padding designed to mitigate accelerations on the brain. With the growing concern for player safety, regulating bodies, like the National Operating Committee on Standards for Athletic Equipment, have implemented standards for protective equipment, including football helmets. On top of these standards, there have been multiple methods developed to assess helmet performance with different testing apparatuses. Manufacturers are interested in how their helmet performs according to multiple testing methods. This could be costly if they do not have the proper testing equipment that a protocol utilizes. This thesis assesses the interchangeability of different test equipment to reproduce a testing protocol. The desire to perform well in testing standards has driven the improvement of helmet performance and continued design innovation. The second aim of this thesis is to evaluate helmet performance and its relationship with design changes in football helmets manufactured between 1980 and 2018. / Master of Science / When football originated in the 1800s, players wore no protective equipment. Between 1869 and 1905, there were 18 deaths and 159 serious injuries attributed to the sport. Following this, players began to wear protective equipment. The first use of a football helmet was in 1893, made of leather and designed to reduce the risk of skull fracture. Initially, football helmets were intended to protect a player against the most severe hits they would experience on the field. More recently, it has been shown that mild traumatic brain injuries, such as concussions, can induce long-term neurodegenerative processes. Since their introduction, helmets have transformed into plastic shells with padding designed to mitigate accelerations on the brain. With the growing concern for player safety, regulating bodies, like the National Operating Committee on Standards for Athletic Equipment, have implemented standards for protective equipment, including football helmets. On top of these standards, there have been multiple methods developed to assess helmet performance with different testing apparatuses. Manufacturers are interested in how their helmet performs according to multiple testing methods. This could be costly if they do not have the proper testing equipment that a protocol utilizes. This thesis assesses the interchangeability of different test equipment to reproduce a testing protocol. The desire to perform well in testing standards has driven the improvement of helmet performance and continued design innovation. Another aim of this thesis is to evaluate helmet performance and its relationship with design changes in football helmets manufactured between 1980 and 2018.

The research presented in the thesis explores the biomechanics of the head and neck during impacts in football. The research related to the head is geared towards advancing the current understanding of the mechanisms of mild traumatic brain injury, specifically by investigating head accelerations experienced by football players during impacts. To do this, a six degree of freedom sensor that could be integrated into existing football helmets and is capable of measuring linear and angular acceleration about each axis of the head was developed and validated. This sensor was then installed in the helmets of 10 Virginia Tech football players and data was recorded for every game and practice during the 2007 football season. A total 1712 impacts were recorded, creating a large and unbiased dataset. No instrumented player sustained a concussion during the 2007 season. From 2007 head acceleration dataset, 24 of the most severe impacts were modeled using a finite element head model, SIMon (Simulated Injury Monitor). Besides looking at head acceleration, the force transmitted to the mandible by chin straps in football helmets was investigated through impact testing. Little research has been conducted looking at the mandible-chin strap interface in the helmet, and this may be an area of helmet design that can be improved. The research presented in this thesis related to the neck is based on stingers. Football players wear neck collars to prevent stingers; however, their designs are largely based on empirical data, with little biomechanical testing. The load limiting capabilities of various neck collars were investigated through dynamic impact testing with anthropomorphic test devices. It was found that reductions in loads correlate with the degree to which each collar restricted motion of the head and neck. To investigate the differences in results that using different anthropomorphic test devices may present, the matched neck collar tests were performed with the Hybrid III and THOR-NT 50th percentile male dummies. The dummies exhibited the same trends, in that either a load was reduced or increased; however, each load was affected to a different degree. / Master of Science

In recent years, concussions and the effect this injury has on the human brain has been an area of concern for many people involved in sports. And perhaps rightfully so, as between 1.6 and 3.8 million people each year sustain a sports-related concussion in the United States. In the past, concussions have been solely linked to transient symptoms; however, recent research suggests that the injury can also result in long term neurocognitive impairment. Thus, there is much needed research to better understand concussions and assist in the development of safety techniques that will reduce the occurrence of such injury. Participants of youth football are at an extreme disadvantage as very little research has been conducted on this population. The research presented in this dissertation attempts to characterize head impact exposure of a variable subgroup of youth football, middle school football, in order to better understand concussions in youth. In addition to better understanding concussions, it is imperative that correct laboratory techniques are developed to accurately simulate realistic head impacts. This dissertation also presents results from the evaluation of current testing procedures that can be used for laboratory testing of sports equipment and simulation of actual field impacts. Evaluation of these techniques will further validate their ability to act as methods for both safety and research in sports injury. Thus, the overall goal of this dissertation is to provide results that will both further understanding of concussions and evaluate the realistic performance of laboratory techniques, influencing informed decisions to reduce the risk of concussions. / Ph. D.

No / The acceleration of electrons and protons caused by a super-Dreicer electric field directed along the longitudinal component By of the magnetic field is investigated. The three-component magnetic field in a nonneutral current sheet occurring at the top of the reconnecting flaring loops on the charged particle trajectories and energies is considered. Particle trajectories in the reconnecting current sheet (RCS) and their energy spectra at the point of ejection from the RCS are simulated from the motion equation for different sheet thicknesses. A super-Dreicer electric field of the current sheet is found to accelerate particles to coherent energy spectra in a range of 10-100 keV for electrons and 100-400 keV for protons with energy slightly increasing with the sheet thickness. A longitudinal By component was found to define the gyration directions of particles with opposite charges toward the RCS midplane, i.e., the trajectory symmetry. For the ratio By/Bz < 10-6 the trajectories are fully symmetric, which results in particle ejection from an RCS as neutral beams. For the ratio By/Bz > 10-2 the trajectories completely lose their symmetry toward the RCS midplane, leading to the separation of particles with opposite charges into the opposite halves from an RCS midplane and the following ejection into different legs of the reconnecting loops. For the intermediate values of By/Bz the trajectories are partially symmetric toward the midplane, leading to electrons prevailing in one leg and protons in the other.

More than 19 million children participate in youth baseball and softball annually. Although baseball and softball are not commonly depicted as contact sports in the, according to the U.S. CPSC baseball and softball were responsible for 11.6% of all head injuries treated in emergency rooms in 2009; third most behind only cycling and football. Ball impact has been identified as the leading cause of injury in baseball and softball, with the most frequent injury resulting from a ball impacting the head. Reduced injury factor balls, infield softball masks, batter's helmets, and catcher's masks have all been integrated into baseball and softball as a means for preventing serious head injury from ball impact. The research in this thesis had four objectives: to compare the responses of the Hybrid III and NOCSAE headforms during high velocity projectile impacts, to compare head injury risk across a range of baseball stiffness designed for different age groups, to evaluate the effectiveness of infielder softball masks' ability to attenuate facial fracture risk, and to describe a novel methodology to evaluate the performance of batter's helmets and catcher's masks. Results of these research objectives determined the most suitable ATD headform to evaluate head injury risk for high velocity projectile impacts, provided a framework for determining the optimal age-specific ball stiffness and optimal infield mask design, and disseminated STAR ratings for batter's helmets and catcher's masks to the public. The research presented in this thesis can be used to further improve safety in baseball and softball. / MS / Baseball and softball are two commonly played sports, however, they combine to yield some of the highest head injury rates among sports. Safety measures like protective headgear and softer balls have been implemented into the games, but there is currently no metric for comparing different models and brands on their effectiveness at reducing head injury. The research in this thesis provides an evaluation system that compares the effectiveness of protective headgear between different models and brands and their ability to reduce head injury. This research is presented to the public as a purchasing tool and can be used to further improve the safety in baseball and softball.

The topic of this thesis is a detailed investigation of different aspects of the particle acceleration mechanisms operating in Collapsing Magnetic Traps (CMTs), which have been suggested as one possible mechanism for particle acceleration during solar flares. The acceleration processes in CMTs are investigated using guiding centre test particle calculations. Results including terms of different orders in the guiding centre approximation are compared to help identify which of the terms are important for the acceleration of particles. For a basic 2D CMT model the effects of different initial conditions (position, kinetic energy and pitch angle) of particles are investigated in detail. The main result is that the particles that gain most energy are those with initial pitch angles close to 90° and start in weak field regions in the centre of the CMT. The dominant acceleration mechanism for these particles is betatron acceleration, but other particles also show signatures of Fermi acceleration. The basic CMT model is then extended by (a) including a magnetic field component in the invariant direction and (b) by making it asymmetric. It is found that the addition of a guide field does not change the characteristics of particle acceleration very much, but for the asymmetric models the associated energy gain is found to be much smaller than in symmetric models, because the particles can no longer remain very close to the trap centre throughout their orbit. The test particle method is then also applied to a CMT model from the literature which contains a magnetic X-line and open and closed field lines and the results are compared with the previous results and the findings in the literature. Finally, the theoretical framework of CMT models is extended to 2.5D models with shear flow and to fully 3D models, allowing the construction of more realistic CMT models in the future.

The one dimensional transient heat conduction equation was numerically modeled through matrix diagonalization and three time-discretization schemes. The discrete methods were first-order backward, second-order backward, and implicit finite difference schemes. All simulations used the central difference formula in the space dimension. Two relevant physical systems were considered: a uniformly conducting slab and a melting block of ice. The latter lead to a moving boundary system, or Stefan problem. The multiphysics of melting was numerically modeled through alternating updates of temperature and melt front profiles. Iterative simulations were run with regularly refined discretization meshes in both systems. In the case of the conducting slab, temperature at a fixed point in space and time was considered. For the Stefan problem, the melt front movement after a set time was the physical solution of interest. The accuracy of the convergent results was increased using Richardson acceleration and the Wynn's epsilon algorithm. Accuracy was improved for the moving boundary problem as well, but to a significantly lesser degree. The relative errors improved by five and two orders of magnitude for the conducting block and melting ice simulations, respectively. These relative errors were used to determine that matrix diagonalization is the most accurate numerical solution among the four considered. In both simulation convergence and acceleration potential, matrix diagonalization was superior to the implicit and explicit discretization solutions. However, matrix diagonalization required significantly more computational time. With the enhancement of convergence acceleration, the finite difference schemes obtained similar relative errors to the diagonalization model. This demonstrated the value of convergence acceleration in the classic dilemma for every programmer. There is always a balance struck between model sophistication, accuracy, and computational time. Convergence acceleration allows for a simpler numerical model to achieve comparable accuracy, and in less time than that required for sophisticated numerical models. The numerical models were also compared for stability through parameters that arose in each simulation. These parameters were the Courant-Friederichs-Lewy (CFL) condition and diagonalized eigenvalues. Though diagonalization was found to be the most accurate, it was determined that the backwards finite difference solutions are the easiest to evaluate for stability. In these solution methods, the CFL value allows the stability to be determined prior to running the simulation.

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

This thesis work is dedicated towards finding a feasible test rig design, which can expose small components, produced by SAAB, to a variety of accelerations under different conditions. A literature study is conducted with the objective of gathering information regarding high acceleration testing, where relevant components, designs and calculation methods are presented. A series of concepts are presented and evaluated against a requirement specification, the first concept iteration concerns the method of acceleration whereas the second and the third concept iterations concerns the design of the test rig on different levels of detail. The third concept evaluation is strengthened by several calculations, which indicates the feasibility of the concept in some manner. One concept achieved the highest score in the third concept evaluation and as such is presented as the best suited concept for further development. / Denna avhandling är dedikerad till framtagningen av en möjlig design för en provningsrigg, som kan utsätta små komponenter, som produceras av SAAB, för flera olika accelerationer under olika förhållanden. En litteraturstudie genomförs med syftet att samla information om provning under höga accelerationer, där relevanta komponenter, designer och beräkningsmetoder presenteras. En serie koncept presenteras och utvärderas med hjälp av en kravspecifikation. Den första konceptiterationen berör metoden för acceleration, medan den andra och den tredje konceptiterationen berör designen av provningsriggen. Den tredje koncept utvärderingen stärks av flera beräkningar, som indikerar konceptets lämplighet ur något perspektiv. Ett koncept uppnådde högst poäng i den tredje koncept utvärderingen och presenteras därav som det bäst lämpade konceptet för vidare utveckling.