Summary

The goal of this project is to obtain the angular and linear velocities required to get a hole-in-one through the most efficient golf swing. The efficiency of the golf swing is characterized by the kinetic energy the ball requires to get the hole-in-one. Another goal was to take weather conditions like the wind into account when modeling the system to mimic a realistic golf swing. The wind affects the trajectory of the golf ball because of the drag it imposes on it. To model this complex system, the golf ball trajectory is broken into three parts. This first part consists of the projectile motion of the ball. This is where aerodynamics has a significant influence on the ball’s trajectory due to drag and lift. The lift caused by the Magnus effect is due to the ball's rotation induced by the golfer’s swing. The loss of angular velocity due to friction between the ball and the air and to a non-uniform flow is also considered to model the physical phenomenon better. Then, the second part models the bounces of the golf ball when it strikes the grass. This is modeled with the restitution equation. The coefficient of restitution between the golf ball and the grass is obtained with the equations from Woo-Jin Roh et al. (2010). The first and second parts are repeated until the ball is no longer bouncing on the grass. The third part models the ball rolling and slowing down due to friction. To simplify the model, a common friction coefficient was used to model the whole golf course. This is easily modifiable if more accurate friction coefficients become available. Once the system is characterized, optimization is done to obtain the most efficient way to swing the golf club while still getting a hole-in-one. To do so, a pattern search algorithm is applied to the system and the objective function minimized is the total kinetic energy induced to the golf ball through the golfer’s swing. A solution for the golf ball's angular and linear velocities is obtained and the resulting trajectory is depicted in the video above.

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***Please consider that the original language of the report is french and the english version is auto-generated using Google Translate***