Launch Velocities in Successful Golf Putting: An Analytical Analysis

Abstract

Background: This study is concerned with the special case of a putted ball intersecting a standard golf hole at its diameter. The velocity of the ball at the initial rim of the hole is termed the launch velocity and depending upon its value the ball may either be captured or it may escape capture by jumping over the hole. The critical value of the launch velocity (V) is such that lesser values result in capture while greater values produce escape. Purpose: Since the value of the V entered prominently in some theoretical studies of putting, the aim of the current study is to provide an original re-evaluation of V and to contrast our results with existing results. Method: This analytical analysis relies on trigonometry in conjunction with Newtonian mechanics and the mathematics of projectiles. The results of a recent study into the mathematics of a bouncing ball which included the notions of restitution and friction were also employed in the analysis. Results: If bouncing and slipping do not occur when the ball hits the far rim of the hole our analysis produces a value of V of 1.356 m/s. When bouncing and slipping are present we find that V is at least 1.609 m/s but increases beyond this value as slipping and friction become greater. Useful relations which relate the dynamics and geometry of the ball to V are provided. Conclusion: Since ambient conditions may influence the extent of bounce and slippage we conjecture that the value of V is not unique.