El Informe del Marqués de Uztáriz (1.785).

Hocknell (2002) reported that, for a given club head speed, the resulting ball speed dropped significantly when impact between club head and ball did not occur at the centre of the club face. Furthermore, changes in impact location can have a significant effect on the trajectory of the ball because of side spin imparted to the ball through the gear effect (Cochran & Stobbs, 1968). Impact location can therefore be regarded as an important factor influencing the efficiency of impact. Changes in shaft stiffness have been associated with shifts in the impact locations for individual golfers (Stanbridge, Jones, & Mitchell, 2004). Therefore, measuring the impact location of the ball along with the other launch variables was considered, with a view to being able to resolve whether potential changes in the launch conditions of the ball were related to changes in club path and orientation or impact location. Being able to resolve the reason for

potential changes may help in understanding the mechanism behind these changes.

At the time of testing, no launch monitor able to report impact location was available, so alternatives were sought. Manual methods for measuring impact location such as impact face tape (Golfworks, USA) or impact spray (as utilised by Stanbridge, Jones, & Mitchell, 2004) were considered but disregarded because of the testing time added by manually registering impact positions after each shot and the unknown effects of these methods on launch conditions. Furthermore, it is inevitable that these methods provide the golfer with feedback regarding the impact location. This feedback would go beyond what the golfer would normally perceive in terms of tactile feedback after impact. Previous authors gave direct feedback to golfers regarding their club head speed and commented that this may have affected the golfers by causing them to focus on achieving maximum club head speed and neglecting other factors (Egret, Vincent, Weber, Dujardin, & Chollet, 2003). Suspecting that a similar effect may occur when providing direct impact location feedback, the possibility of using other methods was investigated.

Williams and Sih (2002) suggested a method that provided no direct feedback and involved no changes to the club face by utilising a three-dimensional motion capture system to measure impact location. After performing a calibration procedure to register the position of the club face relative to three non-collinear markers attached to the butt end of the shaft and the club head, the tee position was determined by placing a reflective ball on the tee. After registering its position, this ball was replaced with a normal golf ball. Following the swing, the data were post-processed to determine the club head path and orientation as well as the impact location. Because this approach allowed the determination of the impact location with minimal interference to the golfer, it was decided to develop a similar club head and impact location tracking system using a three- dimensional motion capture system.

4.6.2.1 Aims of development

The aim of the development process was to design a system that accurately determined the club head path as well as the position of the ball and then combined these sets of data to calculate the impact location on the club face. The system had to meet the following additional conditions:

- Interference with the player‟s swing was to be kept to a minimum. Hence, markers added to the club head had to be small and attached securely.

- With cameras and additional equipment in position, the golfer should not feel restricted in his movement.

- Players should be free to adjust tee position and height, so use of a fixed tee was not acceptable.

- The system needed to operate in an open hitting bay with changing light conditions.

- The player was expected to be able to perform swings at his/her own pace, so the data processing had to be finished seconds after the shots or performed after the test session. The system needed to trigger automatically to allow the player to initiate the swing at any time.

- The number of cameras used for the system had to be kept to a minimum so that there would still be cameras available to record the player‟s body movement.

4.6.2.2 Methods

Based on the aim and the conditions presented above, it was decided to utilise an Oqus 300 (Qualisys, Sweden) camera system for club head tracking. This system consists of infrared cameras operating at a frequency of up to 500 Hz at full resolution (1280x1024 pixels) or at higher frequencies at a reduced resolution. Hence, a trade-off had to be found in terms of temporal accuracy (high frame rate) and spatial accuracy (high resolution). Another compromise

had to be found in terms of capture volume and spatial resolution, as capture volume increases as cameras are moved away from the object but spatial resolution decreases at the same time (Milner, 2008). After pilot tests using tripods and capture rates of 500, 1000 and 2000 Hz, it was decided that a capture rate of 1000 Hz and attachment of the cameras to trussing extending from the lab ceiling would result in adequate data and would avoid interference with the golfer. As only two cameras are necessary to reconstruct the three- dimensional coordinates of a marker, pilot tests were carried out with two cameras. However, it was found that producing redundancy in the acquired data by introducing a third camera increased the robustness of the measurements. Therefore, three cameras were used. An acoustic trigger was placed approximately 1 m from the tee position to provide a trigger signal when registering the sound from the impact of the club head with the ball (see Figure 27).

Figure 27: Setup of custom club head tracking system (cameras: -).

Three reflective markers were attached to the crown of the club and another, self-adhesive flat marker was placed on the ball (diameter of all markers: 5 mm). Players were instructed to place the ball on the tee with the reflective marker facing upwards and aligned with the vertical axis of the global reference system, thereby ensuring that the marker was visible to the cameras. Before each test session, the software Visual3D (C-motion, USA) was utilised to record the offset of the corners of the club face and the face centre relative to the three tracking markers on the club head. It should be noted that the placement of all

three markers on the crown of the club head will result in an increased measurement error when calculating the position of points that are not on the same plane as the marker triad, such as the sole markers on the face. Future studies should consider the use of an additional tracking marker placed on the hosel of the club to avoid this effect.

The cameras were set to collect data continuously before the beginning of each swing, but only camera data from 0.05 sec before receiving a trigger signal from the sound trigger until just after impact was transferred and saved to the computer controlling the camera system.

After labelling the markers, their trajectories were exported to the software Visual3D in order to calculate the trajectories of the virtual offset markers positioned at the corners of the club face and the face centre. Further processing was performed using a number of user-written subroutines in Matlab (Mathworks, USA). These subroutines loaded the face corner trajectories exported from Visual3D and identified the last frame captured before impact for each swing. This frame was identified based on the distance between a plane defined by the face markers and the ball marker (offset by half a ball diameter in the negative z-direction (downwards) and along the x-axis (backwards) to account for the fact that the ball marker was not placed at the contact point between club head and ball but at the top of the ball). The definition of the distance between club face and offset ball marker is illustrated in Figure 28.

Even at a sample rate of 1000 Hz, impact will typically occur at some point between two frames because contact between the club head and the ball only lasts approximately 450 µs (Hocknell, Jones, & Rothberg, 1996). The trajectory of the club head after impact will be influenced by the effects of the impact between the club head and the ball, so only data collected up to the last frame before impact can be used to calculate the impact location. Therefore, the x-, y-, and z-components of the markers defining the corners of the club face were extrapolated beginning from the last frame before impact. The extrapolation was performed by fitting a third order polynomial to the trajectory, neglecting any data collected post-impact, and evaluating the polynomial for each of the desired extrapolation points (see Figure 29). A total of 100 extrapolation points were used; each separated to the next one by one hundredth of the time between frames. These were subsequently used to determine the precise impact time.

Figure 29: Example for results from the extrapolation algorithm.

The impact time was found by calculating the distance between the offset ball marker and a plane defined by the club face markers for each of the extrapolated sets of marker positions. This is a similar method to that used to identify the frame before impact. Once the impact time was found, the impact point was converted from the global coordinate system to a local club face coordinate system in order to determine the impact location on the club face. The club head speed of the centre of the club face in the instant before impact was determined using third order backward finite differences. Extrapolating the trajectory of the face centre to the estimated impact time between frames required the derivation of a backward difference formula for non-uniform step sizes (see Appendix C, p. 205).