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Golfer-Ground Interaction Moments
Moments Acting on the Body during the Swing
Since the arms and the club (and the upper body) mainly move (i.e., rotate) along an inclined swing plane (with some off-plane motions as well), the moments about two axes are absolutely required: the forward-backward (F/B) axis and the vertical axis (Figure 1). According to Newton's 2nd Law of Motion, only the external moments acting on the body can alter the angular momentum of the body. Potential souces of external moments include the external forces acting on the body (such as the ground reaction forces [GRFs] and the gravity of the body) and the external moments directly acting on the body (such as the ground reaction moments [GRMs]). Among these, the gravity acts through the body COM and cannot generate a moment about the body COM. Therefore only the GRFs and the GRMs provide external moments to the body.
Figure 1. The main moment components required in the golf swing: frontal plane (forward-backward axis) and horizontal plane (vertical axis).
External moments can be generated only through the foot-ground interaction (GRFs and GRMs). Every golfer uses the ground during the swing but some use the ground better than others. The quality of the foot-ground interaction is one of the key aspects of the mechanically robust golf swing. The quality is determined by not only the force magnitudes but also their directions. Large GRFs do not automatically mean a good foot-ground interaction. Often times, the swing efficiency is largely determned by the directions of the GRFs, not by the magnitudes.
Moments produced through the golfer-ground interaction can be classified into three groups: the GRF moments, the pivoting moments, and the foot contact moments. The GRF moment is the primary cause of the rotation about the F/B axis, while the pivoting moment is the primary cause of the rotation about the vertical axis.
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GRF Moments
One important aspect of the ground reacton forces (GRF) acting on the golfer's feet is that they generate not only a linear acceleration of the body but also an angular acceleration of the body about the body center of mass (COM) during the swing. When the body is freely moving, the COM of the body is used as the center of rotation (COR) in assessing the angular effect of the golfer-ground interaction.
For example, Figure 2 shows the GRF moments produced by the GRFs acting on the golfer's feet. The GRF moments are those produced by the GRFs about the COM of the body. Figure 2A shows two GRF moments produced by the individual GRFs acting on the feet in the frontal plane (face-on view). The moment produced by the lead-foot GRF about the COM (lead-foot GRF moment) is equal to its moment arm (
) times the magnitude of the lead-foot GRF (
). Moment arm is the perpendicular distance from the COR to the line of action of the force (dotted line). The trail-foot GRF moment thus is equalt to its moment arm (
) about the COM times the magnitude of the trail-foot GRF (
). The moment arm of the trail-foot GRF is almost 0 in this particular case as it passes near to the COM. The frontal-plane GRF moment therefore is mostly coming from the lead foot in this example. Figure 2B, in contrast, shows the combined GRF moment in the frontal plane which is equal to the moment arm of the combined force (d) times the magnitude of the combined GRF (F). The combined moment is equal to sum of the individual GRF moments.
Figure 2. GRF Moments produced by the GRFs about the body COM in the frontal plane: individual moments (A) and combined moment (B).
One thing clearly shown in Figure 2 is that even a vertical GRF can generate a moment about the COM as long as the force vector does not pass through the COM. In other words, pushing the ground down hard can affect the rotational motion of the body/club and thus contributes to the clubhead speed. There is a common misconception that a vertical GRF cannot contribute to the clubhead speed.
The GRF moments are generated in all three planes. As shown in Figure 3, the GRF moment generated by the combined GRF can be assessed plane by plane. In each plane the combined GRF vector forms a moment arm about the body COM and generates a GRF moment. Among the planes, the frontal-plane (face-on view) GRF moment is the largest and its max. value occurs near EDA (Figure 3A). This counterclockwise GRF moment helps rotation of the body/club in the downswing direction. This mechanism is the primary source of the moment about the F/B axis.
The sagittal-plane (side view) GRF moment reaches its max. value at BI (Figure 3B). This moment prevents the body from collapsing forward near the imapct. Like the frontal-plane moment, the horizontal-plane (top view) GRF moment reaches its max. value near EDA (Figure 3C). This counterclockwise moment also promotes rotation of the body/club in the downswing direction. This component is fairly small and has minimal importance. The horizontal-plane moment is developed primarily by the pivoting mechanism, instead of the GRF moment mechanism.
Figure 3. Maximum GRF moments: frontal plane (face-on view; A), sagittal plane (side view; B), and horizontal plane (top view; C). The frontal-plane (F/B axis) moment is the largest when compared to the other planes. Both the frontal-plane GRF moment reaches its max. value near EDA, while the saggital-plane GRF moment reaches its max. value at BI.
Since the moment produced by the combined GRF is a function of the moment arm and the force magnitude, one can increase the moment by lengthening the moment arm and/or increasing the force magnitude. Figure 4 shows the body postures of two touring pros near TB. While the force madnitudes are similar, the lengths of the moment arms are quite different. Player A maintains an upright spine alignment, while Player B's spine is severely incined away from the target. This is mainly because of the pelvis position: i.e., Player B's pelvis is shifted relatively more toward the target.
Figure 4. Body postures of two tour players near TB. Both players' GRF magnitudes are similar but Player A shows a substantially longer moment arm than Player B.
Another important aspect revealed in Figure 4 is that Player A's GRF vector inclines more toward the target. As a result, Player A's GRF vector stays farther away from the body COM and his moment arm is substantially longer. For similar GRF magnitudes, Player A's GRF moment in the frontal plane is substantially larger. The length of the moment arm formed by the combined GRF the key of an efficient swing.
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Pivoting Moments
Both the pivoting moments and the foot contact moments are horizontal-plane moments about the vertical axis, so thay only affect the rotational motions of the body/club about the vertical axis.
The pivoting moments are the moments produced by the individual foot GRFs about the vertical axis that passes through the combined center of pressure (COP) (Figure 5). The pivoting moments shown in Figure 5 are both counterclockwise and promote rotation of the body/club in the downswing direction. The combined pivoting moment (i.e., sum of the individual foot pivoting moments) becomes maximum near EDA as shown in Figure 5. The pivoting moments are the primary source of the moment about the vertical axis (in the horizontal plane).
Figure 5. The pivoting moments generated by the individual foot GRFs about the combined COP in the horizontal plane. By pushing the ground horizontally in different directions, the golfer generates a large moment about the vertical axis. The pivoting moment becomes maximum near EDA.
Resolving the horizontal foot GRFs into the F/B and T/A components (Figure 5) highlights the main source of the pivoting moments. Since the T/A components of the foot GRFs act along the direction of stance, their moment arms against the combined COP are quite short. The moment arms of the F/B GRF components however are substantialy longer, as the sum of these should be equal to the stance width. It is clear that the pivoting moments are generated by the F/B components of the foot GRFs.
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Foot Contact Moments
The foot contact moments are the GRMs directly acting on the feet due to the torsional interactions between the feet and the ground. These moments are the smallest in magnitude among the moments acting on the body during the swing. The foot contact moments act on the feet in the counterclockwise direction in the backswing and in the early aprt of the downswing but turns clockwise near the impact.
Figure 6. The foot contact moments acting on the feet due to the direct torsional interactons between the feet and the ground.
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