Essay on The Physics of Playing Golf

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The impact
During the impact between the club head and the golf ball there is large force acting on the ball which causes it to deform. A player will ideally want to launch the ball in the highest possible speed. The one value we can measure for deformation is the coefficient of restitution (further on as ‘COR’). The COR is defined as the ability of one object to transfer energy to another at impact, between 0.0 for perfectly inelastic collision and 1.0 for perfectly elastic. In golf, it describes the ability of the golf club to transfer energy to the ball at impact. Ideally a player will want higher values of COR. When the ball is easily deformed, there is a higher energy loss and lower value of COR. Typically players use hard-shelled balls that are less easily deformed to keep the value of COR as high as possible. However to decrease the deformation of the ball and thus increase COR a player can decrease the speed of the club before the impact. Chou et al. (1994) shows how impact speed affects COR. At impact speed of 20 ms-1­ the COR was determined to be 0.85. Yet when the impact speed increased to 45 ms-1 the COR fell to 0.78. Similar results were confirmed later by more researchers such as Ujihashi (1994). The COR is however mostly affected by the structure of the ball. Generally there are two types of golf balls on the market. Standard two-piece golf balls usually have a rubber solid centre and hard ionomer cover shell. They are harder to deform, thus the COR is higher and the ball travels bigger distances. The three-piece ball on the contrary is much softer. With a usually rubber centre covered by a rubber windage wrapped in a synthetic balata. This ball is much softer and has lower COR which makes it acquire less distanc...

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...% higher club head speed than a rigid shaft.

Adapted from figure 1 in Milne and Davis (1992)
Penner (2001a) showed while keeping the club head speed and mass constant, the main determinant of the drive distance is the dynamic loft of the club which responsively affects the launch angle of the ball. He found that at keeping the mass at 200g and speed at 45ms-1, the dynamic loft leading to the maximum carry distance is 14.9º while the optimal dynamic loft for achieving greatest drive distances is 10.7º. The second value is significantly lower, because with a lower dynamic loft, the launch angle is lower, thus the ball gets a longer run.

With a constant shaft length and mass and constant mass and dynamic loft of the club head, the launch angle is the main determinant of the drive distance.

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