Dynamics of Golf Discs using Trajectory Experiments for Parameter Identification and Model Validation

Abstract

The trajectories of flying discs are heavily affected by their aerodynamics and can vary greatly. The growing sport of disc golf takes advantage of these variations, offering seemingly endless disc designs to use in a round. Despite the increasing popularity of disc golf, most manufacturers lack a scientific approach to disc design and instead use subjective assessments and inconsistent disc rating systems to characterize disc performance. This leads to more guess work for players. This thesis addresses this issue by presenting a physics-based disc trajectory model optimized using experimental trajectory data, and by exploring the possibility for a standardized disc rating system.

A novel stereo-camera-based methodology was developed to capture three-dimensional initial conditions and trajectories of disc golf throws. This data was used to identify the aerodynamic coefficients of physics-based models. These models included six aerodynamic coefficients that depended on five independent variables. Disc wobble was included as a variable affecting the aerodynamic coefficients for the first time. Its effect on model performance was compared to simpler models, which excluded it. The models used various coefficient estimation methods for parameter identification, including polynomial functions and a recently proposed deep-learning approach. The deep-learning approach modelled some relationships with a neural network, which had the benefit of allowing the model to form the most appropriate relationships without relying on functional approximations. Polynomial functions were also used to augment a model that used coefficients previously determined from computational fluid dynamics. These approaches were validated using experimental trajectory data. The model using a mix of computational fluid dynamics data and polynomial functions showed significant improvement over the baseline computational fluid dynamics model. The complete polynomial approaches resulted in the best performing models and showed good agreement with the validation data. The neural network approaches mostly performed well, but could not beat the pure polynomial approaches. The incorporation of disc wobble as a variable affecting the aerodynamic coefficients showed a negligible improvement over the models that disregarded it. Further model improvement is unlikely without first addressing measurement errors in data collection, particularly pertaining to disc attitude, which is the disc plane's orientation relative to the global coordinate system.

The possibility of a trajectory-based test standard for discs was also explored, highlighting the need to carefully choose standardized initial conditions to evaluate disc trajectories with a wide range of flight characteristics. Possible approaches for quantifying flight numbers were also discussed. Considerations for disc mass, initial spin ratio, and air density were also highlighted as these factors were shown to affect disc flight and can have implications for a testing standard.

This research contributes to the growing work surrounding disc golf, by proposing a capture method for three-dimensional disc golf trajectories and validated physics-based disc trajectory models, and by exploring a standardized disc rating system. This work contributes to the understanding of disc behaviour for both manufacturers and players alike, and propels disc golf towards a more scientifically informed future.