Guerra al Contrabando

Based on the literature review and Study 1, it was hypothesised that players would not adapt their body movement depending on the shaft stiffness of the club they were using. Contrary to this hypothesis, it was found that, depending on shaft stiffness, the wrist angle of the players differed significantly at two out of four downswing events. This may be interpreted as a delayed „wrist release‟ occurring for the l-flex shaft. Delayed wrist action has been found to be a characteristic element of the swings of more skilful golfers, who also achieve higher impact velocities (Zheng, Barrentine, Fleisig, & Andrews, 2008a).

There was very little information regarding the effect of shaft stiffness on wrist kinematics in the literature. One study examined shoulder but not wrist kinematics for 84 golfers and found little effect of shaft flex variations (Wallace & Hubbell, 2001). In a single-subject simulation study, McGuan (1996) demonstrated the need for adaptations in body movement when shaft stiffness was varied. This is supported by the findings from the present study, although it should be noted that McGuan provided little detail as to what changes were necessary to maintain an efficient swing when shaft stiffness was altered.

One limitation of the assessment of wrist joint kinematics in the present study is that it is difficult to validate the accuracy of the obtained angles. Accuracy and precision of the motion capture system were determined prior to the study (see Section 4.5.2, p. 86), but it is also important to ensure that the definition of the local coordinate systems relative to the relevant landmarks is accurate. For example, it can be estimated that an offset17 of the markers relative to the longitudinal axis of the shaft may cause a systematic error of approximately 0.5° in wrist angle for a given club. Yet, as the differences in wrist angles for the two shafts at the grip-vertical and grip-horizontal events were above 0.5° and it is deemed unlikely that the marker placement error was above the levels assumed for this calculation, it is unlikely that the observed change in wrist kinematics was caused by instrumental artefacts. Furthermore, it is likely that instrumental errors like this would have caused a change in the wrist angle at all four downswing events.

Two additional kinematic variables were studied: the orientation of the grip at impact relative to the vertical and the angular velocity of the grip segment at impact. No differences were found for the orientation of the grip at impact, which indicates that players did not adjust the global position of the grip at impact to compensate changes in dynamic loft caused by changes in shaft stiffness. However, there was a main effect due to the shaft factor for the angular velocity at impact. Again, the second finding is contrary to the hypothesis that body

17

Assuming the two markers defining the longitudinal axis of the shaft are placed at a distance of 1.1 m and both markers are placed erroneously 5 mm off the longitudinal shaft axis.

kinematics would remain unchanged when shaft stiffness is altered and will be examined in more detail in the following paragraphs.

The mean difference in angular velocity for the two clubs was 12 °/s (or 0.2 rad/s). In order to estimate the effect of this change on the linear velocity of the club head at impact, the finite centre of rotation of the club segment just before impact was calculated for each trial using an algorithm available in the literature (McCane, Abbott, & King, 2005). Typically, the centre of rotation was located to the right of the player‟s hands (away from the target) at the height of the left hand. Hence, the distance of the tip end of the shaft to the centre of rotation can be estimated to be approximately 1 m. Based on this, it can be calculated that the observed increase in grip angular velocity (0.2 rad/s) would result in an increase in linear club head speed of approximately 0.2 m/s. This tends to support the finding from Section 6.3.3.2 that the speed of the virtual tip marker was approximately 0.1 m/s faster for the l-flex shaft than for the x-flex shaft (see Figure 47, p. 150).

One of the simulations performed by MacKenzie (2005) compared a flexible shaft to a rigid shaft. One of the variables presented was the angular velocity of the grip segment of his model just before impact. MacKenzie found that, for a rigid shaft, angular velocity of the grip segment would increase by 8.95 rad/s (5 %) compared to the flexible shaft when optimising the swing for maximum club head speed and keeping the same torque limits in place for both shafts. MacKenzie explained that this difference was most likely caused by the rigid shaft‟s inability to store and release torque prior to impact. It may be possible to deduce from MacKenzie‟s (2005) findings that a stiffer shaft would rotate at a faster angular velocity at impact than a more flexible shaft. This, however, is contrary to the results of the current study, which indicated that angular velocity decreased slightly by 0.2 rad/s (0.5 %) with increasing shaft stiffness. The discrepancy in the results from the two studies could be explained by a number of factors. For example, players in the current study may have changed the peak torque values acting at some of their joints, whereas MacKenzie‟s model used identical peak torque limits for both shaft conditions. It is also possible that

the optimisation algorithm chosen by MacKenzie selected a different adaptation strategy compared to the players in the current study.

6.5 Summary

Regardless of the level of shaft stiffness, the speed of the club head was found to be underestimated by approximately 0.5 % when shaft bending was not taken into account. This was due to the recovery of the shaft from a lag to a lead position just before impact, which was observed for all recorded swings. This finding was confirmed using the strain data, which showed that in all cases shafts were in the process of changing from lag to lead bending just before impact. Typically, the club head was leading relative to the centreline of the unbent shaft at impact.

When comparing the two shafts, a marginal but statistically significant increase of 0.7 % in club head speed at impact was associated with decreasing shaft stiffness from x-flex to l-flex. Impact location and face angle were not affected by the change in shaft stiffness. A number of factors contributed to the increase in club head speeds for the more flexible shaft. Firstly, wrist release appeared to be slightly delayed for the more flexible shaft; the angle formed by forearm and grip was greater for the x-flex than for the l-flex club at two downswing events. This may have resulted in the increase in angular velocity at impact of the grip segment that was observed for the l-flex compared to the x-flex shaft. However, this effect would not fully explain the magnitude of club head speed increase seen for the l-flex shaft. The recovery process of the shaft just before impact was found to be another contributing factor as it generated more additional speed for the l-flex than for the x-flex shaft. This was evident from the comparison of a virtual and the actual shaft tip marker and the strain data (recovery rate).

Unexpectedly, lead strain at impact was marginally higher for the x-flex club. This is contrary to mechanisms presented previously by Maltby (1995) and would indicate that launch conditions may not be affected by changes in shaft stiffness as predicted in the literature.

Increased bending in the toe-up/down plane was registered for the l-flex shaft at the top of the backswing compared to the x-flex shaft, but it is not known to what extent this affects the behaviour of the shaft just before impact. It was seen that players typically rotate the shaft through 90° when squaring up the club face before impact, so bending in the toe-up/down plane at the top of the backswing would only affect the behaviour of the shaft in the lead/lag plane if the two strain components were coupled. Future studies will need to determine the amount of coupling between the two bending planes.

It is important to point out that the observed changes in club speed were on a very small scale. It is likely that few, if any, golfers would be able to detect their effect. Future studies need to determine whether further modifications of the shafts (e.g. lesser stiffness) would allow golfers to take advantage of the effects. It remains difficult to understand cause and effect in the complex interaction of player and golf shaft, so the next study will utilise a golf robot that is unable to adjust its swing actively when shaft stiffness changes. This may also facilitate a comparison of more direct outcome variables, such as the full set of launch conditions.