No need for the math model...
Canada uses TERPS, hold patterns are a pre-defined racetrack...
FAA Order 7130.3A, “Holding Pattern Criteria,” contains the containment criteria for all FAA holding patterns. The criteria assumptions contained in this order are predicated on a March 31, 1964 order, FAA Handbook AT P 7130.8, “Development of Holding Pattern Criteria and Procedures.” 31 holding pattern templates were developed to fit over 100 different combinations of indicated airspeed (IAS), altitude, and distance from facility in the case of ground-based navaids. Averaged seasonal winds aloft were part of this extensive 1964 evaluation.
For RNP procedures, the templates have been reduced to only 5 choices.