Tenpin bowling is a typical skill sport. During the approach, the movement timing as well as the control of finger and thumb forces is decisive. Movement, finger forces and moments affect the dynamics of the ball, which is classified by three different types of shots:
The ‘straight ball’ is used mostly by beginners and is performed by throwing the ball in a straight line down the lane. The ball thereby rotates about a horizontal axis.
The ‘hook ball’ moves in a smooth arcing motion down the lane. This allows the ball to enter the pocket, between the 1 and 3 pins for right-handed bowlers, at an angle, which maximises the chance to score strikes. The hook ball rotates about a predominantly backward directed axis. Depending on the revolution rate of the ball, bowlers are classified as strokers, tweeners (power strokers) and crankers, the latter producing extreme revolution rates and a more pronounced hook. The hook motion is generated by the increasing friction force at the transition from the oiled to the dry part of the lane which forces the ball to roll left- and forwards and thus to hook.
The ‘spin ball’ rotates about a predominantly vertical axis. The large revolution rate mixes up the pins upon impact to carry the strike.
The identification and measurement of performance indicators in skill sports is a challenge, which is specifically reflected in the poor number of literature sources on performance analysis of ten-pin bowling.
Basically, we can distinguish between general and specific performance indicators. The former are not sports-specific, like physiological and psychological parameters.
Physiological parameters mentioned in the literature are the grip strength with no significant correlation with bowling score 1, the aerobic power index, correlating with the bowling score only in female bowlers 2, and the age, which negatively correlates with the bowling performance (‘less than a 10% decline in the span of 50 years’ 3).
Better bowlers show ‘greater mental toughness, a higher degree of planning and evaluation, greater consistency, more interest in improvement, less use of luck attributions, more confidence in equipment and technique, and greater competitiveness’ 4.
Specific performance indicators can only be assessed through advanced performance analysis, which monitors the performance throughout the sportive exercise, before the traditional result–e.g. winning time, height, distance, score, etc–is available. Advanced performance analysis hinges on the instrumentation of the athletes, the equipment, and the sports facilities.
Chu et al. 5 assessed kinematic parameters, angular displacement and velocity of the arm, with video analysis and identified some significant differences between female and male bowlers. Hon et al. 6 recorded the angular velocity of the swinging arm with an inertia link sensor 7 strapped to wrist. None, of these two literature sources, however, proved that the selected parameters correlate with the bowling score.
The instrumentation of bowling facilities comprises foul detection systems and computer aided tracking systems. The latter record the position of ball release, launch angle, ball speed, breakpoint, and entry angle with ultrasonic sensors mounted on the lane 8.
The instrumentation of the equipment, i.e. of the bowling ball, will be dealt with in this paper. It is the aim of this study to
1.Develop an instrumented bowling ball, which is able to measure the forces and moments applied to the ball by the bowler,
2.Test the ball during the approach, and
3.To identify performance indicators, which correlate, as well as clearly increase or decrease, with the score.
2. Design of the instrumented bowling ball
The basic idea behind the design was to measure the thumb and finger forces, applied to the ball, or more specifically, to the finger and thumb holes. Thus, it was essential to replace these holes by tubes, which are connected to transducers, hidden inside the ball. The transducers, in turn, are connected to the ball itself. A small gap between the shell of the ball and the tubes ensures that all forces applied to the tubes flow through the transducers. The width of the gap must be maintained even under large forces. Furthermore, the grip span needs to be adjustable to accommodate for different bowlers.
The instrumented ball (Figure 1) was designed in Pro/ENGINEER Wildfire 3.0 (Parametric Technology Corporation, Needham MA, USA). Some parts were CNC (computer numerical control) machined after converting their Pro/E files to Pro/MANUFACTURING (Parametric Technology Corporation, Needham MA, USA). A commercially available bowling ball (Columbia 300 Blue Dot, Columbia 300 Inc., Hopkinsville KY, USA) was sawn in half, the core was removed, and an aluminium base plate was inserted between the two halves (Figure 2). The three transducers, one for each finger, were mounted on the base plate through aluminium connectors, the position of which was adjustable along several slots machined into the base plate (Figure 2). The transducers, 6-DOF silicon strain-gauge force sensors (Nano25, ATI Industrial Automation, Apex NC, USA 9), were connected to aluminium tubes, inclined by 29 degrees with respect to the ball's vertical axis, perpendicular to the base plate (Figure 2). During the assembling of the ball, additional weight blocks were added to restore the original weight of the ball and to accommodate for heavy ball strokers and crankers, and light ball spinners. It is important to notice that the transducers are connected to interface power supply boxes by cables. These cables did not compromise the experiments, as, once the ball is released, the fingers no longer applied forces to the ball and thus the ball was not required to roll or skid after release and could be stopped by foam cushions.
The orientation of the sensor coordinate systems is shown in Figure 3. The coordinate system of the ball is: x-axis pointing from ring and middle finger towards the thumb, y-axis from the centre of the ball to a point between the openings of the finger and thumb holes, and z-axis from ring to middle finger. When holding the ball with supinated right hand, thumb in opposition to the fingers, and hanging arm, the ball coordinate system is: x-axis forward, y-axis upward, and z-axis to the right.
Ten male bowlers of different performance and specialisation participated in the experiments (Table 1). Each bowler performed the shots four times to assess repeatability and consistency. The mechanical parameters obtained from the experiments were correlated with the average score of the bowlers, and the coefficients of determination (Table 2) served to identify performance parameters. It has to be noted that beginners performing a type of shot other than the one specialised in will probably have a lower average score for that shot than for the shot specialised in. It is not expected that this fact changes the coefficient of determination significantly. Furthermore, the objective was to compare two expert bowlers with two weaker bowlers for each type of shot.
Table 2. Coefficients of determination (r2) of all parameters with average score (strong correlation if r2>0.64; for all parameters, all correlations are significant at p<0.01) and the change in average score per two residual standard deviations (in parentheses).
Fxball: sum of finger and thumb forces in the x-axis of the ball coordinate system and reaction force of the x-components of inertial and gravitational forces.
Fyball: sum of finger and thumb forces in the y-axis of the ball coordinate system and reaction force of the centrifugal force and the y-component of the gravitational force.
Fzball: sum of finger and thumb forces in the z-axis of the ball coordinate system and reaction force of the z-component of the inertial force.
Fball: resultant of Fxball, Fyball, and Fzball.
Mxball: sum of finger and thumb moments about the x-axis of the ball coordinate system.
Myball: sum of finger and thumb moments about the y-axis of the ball coordinate system.
Mzball: sum of finger and thumb moments about the z-axis of the ball coordinate system.
Mball: resultant of Mxball, Myball, and Mzball.
Pinch force: ratio of 2nd peak to 1st peak
Swing period: ratio of forward to backward swing
Impulse of pinch force: ratio of forward to backward impulse
Fxball 2nd peak
Fyball 2nd peak
Fzball 2nd peak
Fball 2nd peak
Fxball terminal spike
Fyball terminal spike
Fzball terminal spike
Fball terminal spike
Mxball 2nd peak
Myball 2nd peak
Mzball 2nd peak
Mxball terminal spike
Myball terminal spike
Mzball terminal spike
Mball terminal spike
4. Data Analysis
The force and moment data were recorded at 1 kHz and collected with LabView (National Instruments, Austin, TX, USA). Due to the smoothness of the data, filtering was not required. Only for generating the moment vector diagrams, the data were subjected to an eighth order Savitzky-Golay filter with a window width of 21 data points. The effect of this filter corresponded to a low pass filter with a cut-off frequency of 100 Hz. The latter filter, however, shortens the moment spikes and alters the initial and final segments of the data set.
The forces (Fx, Fy, Fz) and moments (Mx, My, Mz) of the thumb, middle and ring finger were processed as follows:
4.1 Resultant Finger Force
The resultant finger force Fd is calculated from
where the subscript d denotes either the thumb, the middle or the ring finger.
After rotating the sensor coordinate system about the x-axis by +29°, i.e. the inclination angle of the tubes (Figure 3),
where the subscripts Th, Mi, and Ri denote thumb, middle and ring finger respectively.
4.2 Forces Applied by the Hand to the Ball (Components and Resultant)
Fxball is the reaction force of the inertial force FI and the gravitational force FG times sin θ (=FG sin θ), where θ is the angle of the ball coordinate system during the swing relative to the ground (Figure 4; 0° if Fxball is pointing forward, 90° if Fxball is pointing downward when holding the ball with a horizontally retroverted arm at the transition from back to forward swing).
Fyball (Figure 4) is the reaction force of the centrifugal force FC and the gravitational force FG times cos θ (=FG cos θ).
The pinch force is
The pinch force vectors at thumb and fingers are by definition in line and opposite to each other, have the same magnitude, and thus are mutual reaction forces.
4.3 Position of the Centre of Pressure COP
The COP position results from
The COP refers to the origin of the resultant force of each finger applied to the finger tubes, and thus to the distance between the origin of the resultant force and the origin of the sensor coordinate system.
Equation (11) implies that
where the atan2 function returns the resultant of the xy-force and the xy-moment in any quadrant (in contrast to the inverse tangent function, which returns the angle in the first and fourth quadrant only).
4.4 Ball Moments
The ball moments (Figure 4) are defined as follows:
Roll (rightward/leftward spin):
Yaw (inward/outward spin):
Pitch (back/top spin):
4.5 Swing Timing and Performance Parameters
The beginning of the backward swing was set to the last point with zero force rate before the first force peak (Figure 5). The transition from backswing to forward swing was defined by the intersection of the gradients of the force-time signal (Figure 5) before and after dead centre. The point between the two force peaks with minimum force was not suitable for defining this transition, as this minimum can appear very early or late between the two peaks, and in some cases more than one minimum was observed. The end of the backswing was defined as the continuation of the last major decrease in force and its intersection with the baseline (Figure 5).
The parameters obtained from the force data are listed in Table 2, and comprise the peak forces and terminal force spikes (Figure 5), moment peaks and spikes, and the ratios of specific back- to forward swing parameters (peak force, swing period and impulse). These parameters were correlated with the average score (listed in Table 1). The parameters were considered to represent bowling performance if the correlation is strong (r>0.8, r2>0.64), and if the performance parameters increase or decrease clearly with the average score. The latter was assessed from the gradient of the linear regression and the linear residual standard deviation. If the latter is large, then a large gradient is not meaningful and does not necessarily indicate an increase within the given range of the independent variable (i.e. the average score). Thus, the change of the average score was calculated from the gradient, which corresponds to two residual standard deviations. The smaller the change of average score per two residual standard deviations, the more a performance parameter increases or decreases with the average score (Table 2).
4.6 Force and Moment Vector Diagrams
The force vector diagram of each experiment was generated and visualised in AutoCAD 2000 (Autodesk, San Rafael CA, USA) by combining the COP and resultant force data. The forces were considered to be applied by the ball to fingers and thumb, however, the force vectors were displayed on the ball (comparable to the Pedotti diagram of gait analysis, or vector diagrams displayed on climbing holds 10). If, however, the forces applied by the human body to the instrumented equipment, i.e. the other way round, were displayed on the equipment, the vectors would intersect instead of fan out and thus compromise the visibility of the vectors and the value of the vector diagram. The single vectors per time step were represented graphically as 4D diagrams, where the time is colour-coded in rainbow colours 10.
Comparable to the force vector diagrams, the moment vector diagrams were generated and visualised in AutoCAD 2000 and equally displayed on the ball, however as regular surfaces instead of single vectors.
The high score is on average 1.52 times higher than the average score. The correlation between average and high score is almost 1 (r=0.999, r2=0.998).
5.2 Swing Timing
The swing period is on average 1.635±0.184 s (range 1.183–2.200 s). The swing period decreases with the average score (r=0.355, r2=0.126), from 80 to 120 by 0.235 s.
The period of the back swing, 1.111±0.186 s (0.8–1.6 s), decreases with the average score (r=0.554, r2=0.306), from 80 to 120 by 0.37 s;
The period of the forward swing, 0.524±0.070 s (0.320-0.622 s) increases with average score (r=0.546, r2=0.298), from 80 to 120 by 0.135 s.
5.3 Finger Forces against Time
The finger forces represent the reaction forces of these ball forces which originate at the centre of mass (COM), i.e. gravitational, inertial and centrifugal forces.
The force time graphs show two peaks in general. The first one is associated with the backswing, the second one is due to the forward swing (Figure 5). The trough in between the two peaks marks the transition from back- to forward swing.
Figure 6 shows the individual finger forces of different shots and performance. The swing timing is apparent in Figure 6, i.e. the period of the backswing is shorter in better bowlers.
Furthermore, it seems that the first peak of the thumb force is far higher than the second one in beginners, compared to expert bowlers. The distribution of middle and ring finger forces, however, shows no correlation with the type of shot or with the performance. Both finger forces can be of equal magnitude (Figure 6d); the middle finger force can be higher than the one of the ring finger in both peaks (Figure 6a), in the first peak only (Figure 6c), or in the second peak only (Figure 6b). In general, expert bowlers were more consistent as to the repeatability of force levels than beginners.
The pinch force shows how tight the pinch grip is. Both the first and the second peak of the pinch force increase with the average score (r2=0.248 and 0.552 respectively). The second peak increases 2.4 times faster with average score than the first one. Below an average score of 174, the first peak is on average higher than second one. Better bowlers thus have a tighter grip, especially during the forward swing. The ratio of second to first peak force increases with the average score in all three types of shots (Figure 7), with a high coefficient of determination (Table 2). The same applies to the ratio of forward to backward swing period and impulse (Figure 7, Table 2). The coefficient of determination of the pinch impulse ratio is slightly higher than the one of the pinch force ratio.
5.4 Ball Forces against Time
The magnitude of the second peaks of Fxball, Fyball, Fzball, and Fball, correlates well with the average score (Table 2).
As mentioned above, Fxball is the reaction force of the inertial force FI and the gravitational force FG times sin θ (=FG sin θ), where θ is the angle of the ball coordinate system during the swing relative to the ground (Figure 4). Thus, Fxball corresponds to the acceleration during the forward swing. Better bowlers produce a higher acceleration during the forward swing, which results in a higher ball velocity. The linear ball velocity, in turn, is reflected in the angular velocity of the ball-arm system and therefore in the centrifugal force of the ball. The larger the velocity and consequently the centrifugal force, the larger is Fyball.
Fzball is negative, corresponding to a leftward acceleration in right-handed bowlers. This force component is probably due to the clockwise rotated trunk during the swing.
Higher second peaks in better bowlers do not only apply to the ball forces but also to the resultant finger and thumb forces in general: higher velocity and acceleration during the forward swing and larger inertial and centrifugal forces. The latter two forces, however, are not reflected in the pinch force; nevertheless, the pinch force follows the same pattern.
The magnitude of the terminal force spikes of Fxball, Fyball, Fzball, and Fball, correlates with the average score (Table 2) as well. However, the terminal force spikes of Fxball and Fball show only a medium correlation with the average score. These force spikes are responsible for the moments imparted to the ball immediately before release. In general, hook shots show the highest spikes, followed by straight and spin shots (Figure 8). In hook shots, the spikes are clearly separated from the second peak, whereas in spin shots, they are integrated in the second peak and thus hardly visible (Figure 8).
5.5. Ball Moments against Time
Independent of the type of shot, the Mball moment spike (Figure 9) before release increases with the average score, better bowlers impart larger terminal moments to the ball. The Mball moment spike shows a strong correlation with the average score (Table 2). The terminal Mball moment spike is due to the Mzball spike, which is negative and thus produces a forward spin. In the straight shot, there are small and inconsistent Mxball and Myball spikes, which do not correlate with the average score.
Terminal larger Mxball and Myball moment spikes occur only in the hook shot (Figure 9b, c), which show a strong correlation with the average score (Table 2). The Mxball spike is larger than the Myball one. Myball produces an outward spin, whereas Mxball causes a leftward spin (in right handers). Hence, in contrast to the pure horizontal axis in the straight shot (Mzball spike only) the moment axis in better bowlers points to the left, downward, and backward (right handed bowler).
In expert bowlers with an average score of 200, the three terminal moment spikes (Mxball, Myball, Mzball) of the hook shot are Mybal=−1 Nm, Mxball=−4 Nm, Mzball=−8 Nm (Figure 9c). In weaker bowlers, Mzball=−3, and the other two spikes are almost nil (Figure 9d). Thus the hook shot moment spikes of weaker bowlers are comparable to the straight shot.
In the spin shot, the moment-time graphs are dominated by moment peaks in the second half of the forward swing. In order to rotate the ball about a near-vertical axis, the bowler applies a positive moment and angular momentum by pronating the hand in the second half of the forward swing (Figure 9e,f). The positive Myball is thereby accompanied by a negative Mxball, which might be due to the nature of pronating the hand, possibly generated by additional wrist movements (flexion, extension, abduction). Myball and Mxball produce approximately the same angular impulse of 0.9 Nms in better bowlers. The Mzball peak in the second half of the forward swing is negative in better bowlers and positive in beginners. The peak moment of Mxball and Mzball occurs after the Myball moment peak in better bowlers (Figure 9e), whereas in beginners, the three peaks occur approximately at the same time (Figure 9f).
Additionally, Mzball shows a negative moment spike before release (Figure 9e,f) with an angular impulse of approximately one fifth of Myball in better bowlers. Immediately before release, the negative z-axis is pointing rightwards as the ball has been rotated by 180 degrees. The moment peaks and spikes show a strong correlation with the average score (Table 2). Better bowlers impart larger moments to the ball.
5.6 Force and Moment Vector Diagrams
The principles of 3D vector diagrams are explained in Figure 10. The diagrams can be displayed as single subsequent vectors, one per time step (force vectors; Figures 10 and 11), or as regular surfaces (moment vectors; Figures 10 and 12). With the time colour coded, the vector diagrams become four dimensional (4D). This allows distinguishing between peaks and terminal spikes of forces and moments.
In the 4D force vector diagrams, weaker bowlers show smaller forces, which do not fan out as much as in better bowlers (Figures 11 and 13). The force peaks of back and forward swing can be distinguished from the colour of the force vectors: between green and cyan in the back swing, and magenta in the forward swing. The first peak is clearly larger than the second one in weaker bowlers. The terminal force spikes cause the vectors to fan out, especially in the better bowlers, and in hook and spin shots. These inclined vectors impart the appropriate moments to the ball before release. In general, the terminal force vectors of the ring finger are not larger than the ones of the middle finger. In the spin shot, the vectors of the first and second force peaks are clearly separated, with the second peaks rotated clockwise with respect to the first peaks (top view, Figure 11). This clockwise rotation increases the moment arm of the force vectors which thus produce the counter-clockwise (positive) Myball.
In the 4D moment vector diagrams, the weaker bowlers can be easily distinguished from the better ones (Figure 12): better bowlers produce larger moments. The straight shot is dominated by two moment vectors in opposite direction, with positive and negative Mzball components (clearly visible in top and front views). The positive vector occurs earlier and corresponds to the forward swing, which imparts a backspin moment to the ball. The negative vector corresponds to the terminal moment spike, which imparts a topspin moment to the ball. In weaker hook bowlers, the moment vector diagrams are no different from the straight shot, as far as the terminal moment spike is concerned. The earlier moment vector with a positive z-component is slightly more inclined than in the straight shot. Better hook bowlers show large moment vectors fanning out continuously during the last third of the forward swing. The spin shot, although the terminal negative z-spike is still present, is dominated by the positive Myball peak in the second half of the forward swing.
The instrumentation of sports equipment is often constrained by the rules issued by the governing sporting bodies 11. According to the bowling rules, a tenpin bowling ‘ball shall be constructed of solid material …without voids in its interior and be of a non-metallic composition’ 12. Consequently, an instrumented ball can only be used for training purposes, specifically for performance analysis, and for optimisation of training with biofeedback methods.
The instrumentation aimed at in this project was successful, as the ball is able to measure the individual finger forces as well as the forces and moments applied to the ball by the bowler. Further improvements, however, are necessary, in order to compare the performance indicators to the actual score. Consequently, wireless data transfer and reduction of the gaps between the finger tubes and the shell of the ball are required. The latter enables the ball to roll smoothly, however, compromises the modular design. The grip span can no longer be adjusted, which calls for a range of different hemispherical shells with varying distance between the finger and thumb holes. Furthermore, it would be advantageous to change the radii of gyration (RG) and the RG differential in modular designs.
Apart from the weight of the ball, the grip span, RG and RG differential are the key parameters, which depend on the preference of the bowler. Crankers and strokers prefer a heavier ball, spinners use a lighter one. Smaller RGs and moments of inertia make the ball spin faster. The RG differential is the difference between the RG about the ball's principle axis, and the RG about the axes perpendicular to the principle axis. The larger the RG differential, the higher is the track flare potential. The movement of the oil track on the ball with every revolution increases the friction between the ball and the lane which causes the ball to hook more.
The instrumented ball allows the identification of performance parameters. The latter must correlate with the traditional method of measuring the sport success. The majority of the parameters analysed correlate strongly with the average score in all three shots (Table 2). Astonishingly, better bowlers have a longer forward swing period in spite of higher swing velocities and accelerations. This seems counterintuitive at first glance, yet becomes evident when considering the larger shoulder angles of better bowlers. The change in average score per two residual standard deviations is smaller than 50 in all parameters identified, and smaller than 25 in 50% of all parameters (Table 2). This indicates that an increase or decrease of a performance parameter within a window of an average score of 50 (or 25) is larger than the residual standard deviation.
The peak forces as well as the terminal force spikes applied to the ball during the forward swing are generally larger in better bowlers. The individual moments, Mxball, Myball, Mzball, correlate with the average score only in the spin shot, whereas the resultant moment, Mball, correlates in each type of shot (Table 2). Mxball and Myball terminal spikes correlate only in the hook shot, whereas the Mzball spike correlates in each shot. The positive Fxball spike produces the negative Mzball spike. In the hook shot, the decisive moment is the Mxball spike (negative in right handed bowlers), which forces the ball to roll leftward if friction with the lane increases. However, the ball's precession, which is clockwise from top view, moves the rotation axis from negative x to negative z, such that the ball finally rolls forward when hitting the pocket. The angular velocity of the precession equals the vector product of the ball's spin velocity and the torque applied to the ball by the friction. These principles are responsible for the ball's hook motion. The negative Mxball spike is missing in weaker hook bowlers (Figure 12).
The 4D force and moment vector diagrams are a useful tool for the trainer and the athlete, especially for the assessment of consistency. Apart from general use of force vector diagrams in gait and running analysis, they proved to be a valuable tool in sport climbing 10. In addition to force vector diagrams, moment vector diagrams were introduced for the first time in this bowling project. The advantage of 4D vector diagrams lies in the fact that they combine the magnitude, direction and the time in a single diagram.
The instrumented ball developed is a useful tool for performance analysis. Better bowlers
(a)apply larger forces to the ball during the forward swing and thus move and accelerate faster
(b)have larger ratios of
pinch force of forward swing to pinch force of backswing