Optimal design for disc golf by computational fluid dynamics and machine learning

In this article, we introduce a computational methodology for golf disc shape optimization that employs a novel disc shape parameterization by cubic B-splines. Through application of batch Computational Fluid Dynamics simulations and Machine Learning, the disc parameterization yields functional relationships-so-called shape surrogate models-between the flying rotating disc shape and its flight characteristics. The shape surrogate models facilitate free and constrained optimization in both single- and multiobjective settings, such that both aerodynamic (drag and lift) and structural (mass and moment of inertia) features of the disc are addressed simultaneously. Further, the Professional Disc Golf Association rules for permissible golf discs can be cast as nonlinear constraints for the computational optimization problem. The proposed numerical optimization method yields disc drag coefficient values as low as 0.48 (unconstrained) and 0.52 (constrained) and lift coefficient values as high as 0.26 (unconstrained) and 0.19 (constrained). The presented numerical optimization results also describe the many design tradeoffs between the discs that target long flight range (so-called drivers) and the discs that target flight at low speeds (so-called putters). Moreover, novel optimal rule compliant designs are presented for driver-type and putter-type discs, as well as their compromise, the so-called mid-range discs.