Time-optimal path planning in high winds for a turning-rate constrained UAV is a challenging problem to solve and is important for deployment and field operations. Previous works have used trochoidal path segments comprising straight and maximum-rate turn segments, as optimal extremal paths in uniform wind conditions. Current methods iterate over all candidate trochoidal trajectory types and select the one that is time-optimal; however, this exhaustive search can be computationally slow. In this paper, we introduce a method to decrease the computation time. This is achieved by reducing the number of candidate trochoidal trajectory types by framing the problem in the air-relative frame and bounding the solution within a subset of candidate trajectories. Our method reduces overall computation by 37.4% compared to pre-existing methods in Bang-Straight-Bang trajectories, freeing up computation for other onboard processes and can lead to significant total computational reductions when solving many trochoidal paths. When used within the framework of a global path planner, faster state expansions help find solutions faster or compute higher-quality paths. We also release our open-source codebase as a C++ package. The website and demo can be bound at https://bradymoon.com/trochoids, codebase at https://github.com/castacks/trochoids, and video at https://youtu.be/qOU5gI7JshI .
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