On the flight of a golf ball in the vertical plane

Abstract

The equations of motion for a ball moving in a vertical plane are used to calculate flight paths for a typical golf ball subjected to a variety of launch conditions, spin rates, atmospheric parameters, and wind fields. Time histories of the ball's velocity, flight-path angle, height, range, and spin rate between tee and first impact illustrate that lift induced by the ball's spin has a significant effect on driving range, actually causing the flight-path angle to increase during the first few seconds of flight. While light winds have the expected effects, heavy tailwind is shown to spoil the carry of the ball. Linearized sensitivity analysis indicates that wind uncertainty is an important contributor to impact range and time uncertainty.