Acceleration of clubhead

Below we will analyze and present the acceleration of the clubhead as it is experienced in a two segment model of the golf swing. Fig1 shows the two segments and the trajectory of the clubhead. There is a constant torque applied throughout the down swing, including through and past 'impact'. No active torque at the wrist joint. A passive 90 deg deadstop is programmed in the model to prevent back-knifing.

Fig1

The acceleration of the clubhead is a vector quantity. Its magnitude for the two segment model is given by relation (1).

The acceleration can be decomposed into a normal component and a tangential component. These are given by relations (2) and (3).

The tangential and normal components of the clubhead acceleration are shown in Fig2.  We have inserted a vertical line (green) to indicate when the two segments align. The maximum value for the normal acceleration, zero acceleration for the tangential acceleration, and alignment of segments, don't happen at exactly at the same moment but occur however very close together.

Fig2

A somewhat more interesting intuitive representation of the accelerations is given by a direct vector presentation of the information as done in Fig3 for the total acceleration. Except for the early part of the down swing the acceleration is virtually aligned with the club shaft.

Fig3

There are various way to decompose the acceleration above in two orthogonal components, for instance relative to the club shaft or relative to the line going through clubhead and inner center. However the most logical decomposition is relative to the path of the clubhead. Hence truly the tangential and normal component with respect to the instantaneous radius of curvature. These two accelerations, the normal and tangential components, are shown respectively in Figs 4 and 5.

Fig4

Notice that the maximum normal acceleration vector and segments are linging up together as indeed should be expected.

Fig5

It is perhaps a bit counter intuitive but the maximum tangential acceleration happens somewhere halfway in the down swing and reaches zero, very close to where the two segments align. Beyond the inline situation there is a sign reversal for the tangential acceleration and hence braking and slowing down of clubhead.

It is important to realize that the model has a large constant torque applied throughout the whole down swing but at the bottom the clubhead has  minimum acceleration, reaching virtually zero when segments align. Something to ponder for those who feel that a golfer's effort will increase the acceleration of the clubhead through impact and hence somehow increase the force exerted on the ball or perhaps increase the effective mass of the clubhead.

Fig6 shows the total, the normal, and the tangential acceleration together for a more convenient browsing.

Fig6

mandrin