Abstract
Changes to the Rules of Golf for 2019 allow a golfer to make a stroke from the putting green with the flagstick unattended in the hole. Such an action would previously incur a penalty. This work provides a model framework for the interaction among the ball, hole, and flagstick. The model is based in part on earlier work by Holmes, who examined the ball without the flagstick as allowed under the former rules. The interaction of the ball with the hole/flagstick area is evaluated for whether the ball is holed and for the final distance from the hole in the case of a miss. The flagstick is found to be of mixed benefit, performing more as a backstop as the impact with the flagstick becomes more central (head-on). Glancing blows at higher input angles are found to cause missed shots at lower velocities. Putts that are too fast to be made whether the flagstick is in or out of the hole are found to rest closer to the hole with the flagstick present. The implications are that shots for which the line of putt is better known (increasing the odds of central impact) and where speed may not be well controlled (e.g., greenside pitch shots) benefit from having the flagstick in the hole.
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Notes
If the ball center of mass is below the surface of the hole, the contact point will lie at \((x_c,y_c,z)\). However, the case of contact with the ball center of mass below the hole edge leads to capture of the ball and is thus not considered here.
An angled flagstick will change this assumption.
This is the sort of transition which leads to a putt exiting the hole on a horseshoe-shaped trajectory.
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