upheld these findings (Jenkins, 1947; Noble & Bahrick, 1956; Provins, 1957). Many years ... Responses such as batting a baseball or hitting a tennis ball, as well.
Motor Control, 2012, 16, 19-30 © 2012 Human Kinetics, Inc.
Examining Impulse-Variability in Overarm Throwing M.A. Urbin, David Stodden, Rhonda Boros, and David Shannon The purpose of this study was to examine variability in overarm throwing velocity and spatial output error at various percentages of maximum to test the prediction of an inverted-U function as predicted by impulse-variability theory and a speed-accuracy trade-off as predicted by Fitts’ Law Thirty subjects (16 skilled, 14 unskilled) were instructed to throw a tennis ball at seven percentages of their maximum velocity (40–100%) in random order (9 trials per condition) at a target 30 feet away. Throwing velocity was measured with a radar gun and interpreted as an index of overall systemic power output. Within-subject throwing velocity variability was examined using within-subjects repeated-measures ANOVAs (7 repeated conditions) with built-in polynomial contrasts. Spatial error was analyzed using mixed model regression. Results indicated a quadratic fit with variability in throwing velocity increasing from 40% up to 60%, where it peaked, and then decreasing at each subsequent interval to maximum (p < .001, η2 = .555). There was no linear relationship between speed and accuracy. Overall, these data support the notion of an inverted-U function in overarm throwing velocity variability as both skilled and unskilled subjects approach maximum effort. However, these data do not support the notion of a speed-accuracy trade-off. The consistent demonstration of an inverted-U function associated with systemic power output variability indicates an enhanced capability to regulate aspects of force production and relative timing between segments as individuals approach maximum effort, even in a complex ballistic skill. Keywords: biomechanics, motor control
Force regulation is a central feature of skillful motor behavior because all volitional movement results from muscle exerting force on the segment to which it inserts. Research examining force regulation dates back over one hundred years, originating with a study by Fullerton and Cattell (1892). The aim of this study was to assess the within-subject variability in force during a simple elbow-flexion task against a spring dynamometer over a range of criterion force levels (2-16 kg). Results indicated variability in the force generated increased as the magnitude Urbin is with Auburn University—Department of Kinesiology, Auburn, AL. Stodden and Boros are with Texas Tech University—Dept. of Health, Exercise and Sport Science, Lubbock, TX. Shannon is with Auburn University—Department of Educational Foundations, Leadership, and Technology, Auburn, AL. 19
20 Urbin, Stodden, Boros, and Shannon
of force increased, but at a less than proportional rate. Subsequent investigations upheld these findings (Jenkins, 1947; Noble & Bahrick, 1956; Provins, 1957). Many years later, impulse-variability theory (Schmidt, Zelaznik, Hawkins, Frank, & Quinn, 1979) was developed to make modifications to the existing view of the relationship between speed and accuracy in rapid limb movements, as originally proposed by Fitts’ Law (1954). This model predicts that variability in limb trajectory is a consequence of variability in the initial muscular impulses used to propel the limb through space. That is, the terminal spatial location of the limb results from variability in all of the accelerative forces acting in the plane perpendicular to the desired movement endpoint. An early, significant assumption of this theory, supported by the available research at that time, was that aggregate variability of all of these forces is linearly related to the level of force produced (Schmidt et al., 1979). Sherwood and Schmidt (1980) proposed modifications to this theory after discovering variability in static and dynamic force production peaked as force approached 65% of subjects’ maximum capability, and then decreased as forces were further increased to approximately 92% of maximum. As such, an inverted-U function was found to exist between force magnitude and force variability. Newell and Carlton (1985) later questioned this inverted-U trend citing the lack of control over the time a subject was given to achieve maximum force. Data derived from their experiment demonstrated the maximum force achieved within 400 msec may be more than double the maximum force achieved within 100 msec. With temporal constraints in place, a negatively accelerated function was found to exist between force magnitude and force variability. Consequently, Sherwood, Schmidt, and Walter (1988) followed-up with another experiment where time to peak dynamic force was held constant in each of six load conditions. A linear increase in force variability occurred over the first four load conditions, but decreased slightly over the two highest load conditions. Though there was not significant quadratic trend, a curvilinear relationship was observed. This led Sherwood et al. (1988) to conclude that the criticisms of Newell et al. (1985) were relevant to muscular contractions involving isometric force production. In addition to the aforementioned studies regarding force variability, other research prior and subsequent to the development of impulse-variability theory indirectly supports the notion that decreased temporal and spatial variability is associated with greater force production. In a series of studies where subjects were instructed to project an object along a trackway to intersect the path of another moving object, both temporal consistency and accuracy improved with increased movement velocity. The within-subject standard deviation of movement time was approximately 44% less for maximal-effort movements across all movement distances tested (Schmidt, 1969a, 1969b, 1969c). Additional research by Newell, Hoshizaki, Carlton, and Halbert (1979) upheld these findings, as the movement time with the shortest duration (i.e., 100 msec) over a fixed distance, yielded greater temporal consistency compared with movement times of 500 and 1000 msec. Later research rendered additional support for the finding that temporal and spatial errors decrease as movement time is decreased or the average velocity of the movement is increased (Jasiewicz & Simmons, 1996; Newell, Carlton, Carlton, & Halbert, 1980; Newell, Carlton, & Kim, 1994; Newell, Carlton, Kim, & Chung 1993; Schmidt & Sherwood, 1982). Given that a decrease in movement time over a fixed distance requires an increase in the accelerative forces necessary to propel the limb through
Impulse Variability Theory and Overarm Throwing 21
space, the aforementioned studies provide evidence that near maximal or maximal force production results in decreased temporal and spatial output variability. Overall, the preponderance of evidence discussed to this point counters the notion of a linear relationship between force magnitude and the resultant variability in ballistic, single-joint movements. Notwithstanding this evidence, there is no data to support this relationship in ballistic, multijoint movements where ballistic force generation and timing of segmental interactions are simultaneously altered with increased effort. The impulse-variability theorists (Schmidt et al., 1979) highlighted the importance of applying principles derived from laboratory motor tasks to appreciably more complex, multisegment movements. In this paper, they state, “We feel that these principles, in addition to being fundamental to the understanding of movement control in rapid tasks, have a number of possible areas of application. Responses such as batting a baseball or hitting a tennis ball, as well as responses in which objects are hurled, are similar to the rapid-timing task in that the accelerative impulse is all that is really important, with deceleration occurring after some critical point in the move (e.g., striking or releasing the ball).” p. 438. Ballistic, multijoint movements (e.g., kicking, striking, and throwing) inherently demand high force/power output. Impulse-variability theory is relevant to these movements because of the ballistic nature of the force acting to produce the movement. In these movements, there is also a need to optimally time successive segmental accelerations to produce maximum projectile velocities (Jegede, Watts, Stitt, & Hore, 2005; Stodden, Fleisig, Stodden, Fleisig, McLean, Lyman, & Andrews, 2001; Stodden, Fleisig, McLean, & Andrews 2005). Empirical evidence indicates that increases in throwing speed within highly skilled and lesser skilled throwers is achieved through increases in kinetics, decreases in the absolute time from stride foot contact to ball release, and optimization of timing peak segmental angular velocities (Jegede et al., 2005; Stodden et al., 2001; 2005; Stodden, Langendorfer, Fleisig, & Andrews, 2006). This evidence, taken together with the laboratory research surrounding impulse-variability theory, seems to suggest that variability in the systemic power output of ballistic, multijoint movements (e.g., ball velocity) may decrease as an individual approaches maximal effort. In essence, increasing the force produced by various segments in the kinetic chain, decreasing the absolute time to accelerate the ball, and optimizing the timing between segmental interactions may result in decreased variability. However, the extent to which previous research focusing on impulse-variability theory can be generalized to ballistic skill performance is not understood. Therefore, the primary objective of the current study was to examine the relationship between percentage of maximum overarm throwing velocity and resultant variability. A secondary objective was to examine the relationship between percentage of maximum overarm throwing velocity and resultant error in the terminal spatial location of the projectile.
Materials & Methods Subjects Eight women and 22 men lacking musculoskeletal injury that would affect throwing performance participated in the study (M = 22.4 years). Permission to conduct the study was obtained from the University’s Human Subjects Review Board and all subjects provided informed consent.
22 Urbin, Stodden, Boros, and Shannon
Apparatus A target containing a 1 × 1 cm centroid was constructed on a gymnasium wall 180 cm above the ground. An octagonal target area with 20cm side lengths was oriented around this centroid, and the vertical and horizontal axes were marked. This target was used to provide a global reference goal for subjects and to maintain a consistent throwing direction. Throwing velocity was measured with a Stalker Pro II radar gun (Stalker Inc., Plano, TX) and interpreted as an index of overall systemic power output (work per unit time), which is indicative of both force production and absolute time of force production.
Procedures After providing informed consent, subjects completed a general 5-min warm-up on a cycle ergometer. Following the general warm-up, a self-paced throwing warm-up, progressing to five maximum-effort throws ensued. Maximum throwing velocity for each subject was determined from these last five throws and was set as the highest velocity the subject could produce at least twice. This criterion ensured subjects’ maximum velocity was reproducible and not based on a spurious velocity due to an anomaly in mechanics. Subjects were placed into one of two groups (skilled n = 16; unskilled n = 14) for data analysis based on a criterion measure of maximum throwing velocity (males ≥ 28.0 m/s, females ≥ 22.8 m/s). Criterion velocities for determining skill classification was derived from pilot data from a sample of 198 18–25 year old adults (79 men & 119 women) who demonstrated the most developmentally advanced throwing profile (3–3-3) composed of trunk, humerus, and forearm components (Roberton & Halverson, 1984). Average ball velocities, as well as group minimum and maximum velocities at each percentage of maximum, are contained in Table 1. Immediately following maximal velocity testing, seven percentages of maximum velocity (40, 50, 60, 70, 80, 90, and 100%) were calculated for each individual, and served as target velocity conditions. Subjects performed ten throwing trials with the intent of throwing at each specified target velocity, resulting in 70 total trials for each subject. Target percentage of maximum velocity order was structured by Table 1 Descriptive Statistics for Throwing Velocity (m/s) across Percentage of Maximum in Skilled and Unskilled Subjects. Percent Max
40%
50%
60%
70%
80%
90%
100%
Skilled (n = 16) mean minimum maximum
13.19 11.62 15.19
16.62 14.31 19.22
19.84 16.99 23.25
22.86 20.12 26.82
26.43 22.79 30.85
29.76 25.93 34.42
33.05 28.61 38.45
Unskilled (n = 14) mean minimum maximum
8.37 5.81 10.73
10.57 7.15 13.86
12.55 8.49 16.31
14.66 9.83 19.22
16.73 11.62 21.90
18.99 12.96 24.59
20.92 14.31 27.27
Impulse Variability Theory and Overarm Throwing 23
way of a random number generator. Velocity conditions were organized into ten blocks of seven trials each, with one trial at each percentage of maximum velocity occurring once within each block. Subjects then performed, in succession, ten blocks of seven trials. The first block of trials was used to familiarize the participant with the task of throwing at each specific velocity percentage. Consequently, data from this first block were not used for analysis. Prior to each trial, subjects were verbally instructed to throw at the specified percentage of maximum velocity within each block. Following each trial, subjects were informed of their actual throwing velocity in miles per hour. After each block of trials, radial error measurements were recorded. Subjects were allowed to rest at self-selected durations during this time to minimize fatigue.
Statistical Analysis ∑ ( x i − M ) on the nine trials for each specified velocity percentage were averaged and used for statistical analyses. Data for all subjects were analyzed using a repeated-measures ANOVA to determine within-subject variability across all subjects. Bonferroni post hoc tests were performed to examine differences in variability at each percentage of maximum. A 2 (skill level) × 7 (condition) mixed model repeated-measures ANOVA was used to examine velocity variability between skilled and unskilled groups. In addition, independent samples t tests were performed to detect differences between skilled and unskilled groups at each percentage of maximum.
Velocity Variability. Variable error
2
Spatial Error. Analyzing spatial error required a different statistical procedure
because subjects’ throwing velocity sometimes crossed into other criterion percentages of maximum due to limited velocity ranges between percentages of maximum. Thus, the resulting spatial error was not always representative of the specified criterion velocity (see Limitations). Spatial error (radial error) was examined over the entire range of throwing velocities for each subject (i.e., 63 throws for each subject). These continuous data allowed a sensitive discrimination of spatial error across the entire spectrum of force. A mixed model regression procedure with a compound symmetry covariance structure was used to assess the relationship of percentage of maximum velocity and resulting spatial error (Stodden et al., 2001, 2005). In essence, the mixed model regression analysis examined all 30 velocity/spatial error regressions (one per subject) to determine if there was a consistent effect among all subjects. Significance for all analyses was set at the .05 level
Results Velocity Variability Mean variable error for velocity (m/s) as a function of each percentage of maximum across skilled and unskilled subjects is shown in Figure 1. The repeated-measures ANOVA (7 repeated conditions) with built-in polynomial contrasts revealed a strong quadratic fit for all subjects with variability in throwing velocity increasing from 40% to 60% of maximum, where it peaked, and then decreasing at each subsequent interval to maximum (p < .001, η2 =
24
Figure 1. Mean variable error (m/s) of throwing velocity as a function of percentage of maximum effort in skilled and unskilled subjects.
Impulse Variability Theory and Overarm Throwing 25
.555). Bonferroni post hoc tests revealed significant differences between 50% and 100%, 60% and 100%, 70% and 100%, 80% and 100%, 90% and 100%, as well as 40% and 60% of maximum. The mixed model repeated-measures ANOVA indicated that, although both skilled and unskilled groups demonstrated similar significant inverted-u trajectories in variability (p < .001 and p = .03, respectively) that aligned with the overall model fit (see Figure 1), the unskilled group demonstrated significantly less variability overall (p = .037). The independent samples t tests indicated variability between skilled and unskilled groups was significant at 70% of maximum (p = .026) and 100% of maximum (p = .028). The remaining percentages of maximum failed to reach significance; however, the p values for most comparisons approached .05 (p values ranged from .075 to .104) with the exception of 90% of maximum (p = .681). Skilled performers demonstrated less variability than nonskilled subjects at maximum effort.
Spatial Error Results from the mixed model regression procedure indicated there was no significant linear relationship between percentage of maximum velocity and resulting spatial error (F = 0.41, p = .5226). Mean radial error across the range of percentage of maximum velocity across all subjects is shown in Figure 2.
Discussion The finding of an inverted-U relationship between percentage maximum throwing velocity and resultant variability, despite the lack of control over movement time, supports the early work of Sherwood and Schmidt (1980). Hypothesized modifications in absolute time for accelerating segments and/or relative timing among segments in throwing at different percentages of maximum throwing velocity may have synergistically interacted with increases in force production, which was demanded by the intent to throw at greater percentages of maximum. The increase in systemic force output requirements resulted in more consistent velocities at maximal or near maximal thresholds of performance. Greater systemic force output in throwing, as evidenced through increased ball velocity, may have been associated with less time to produce the movement and optimization of segmental interactions (Stodden et al., 2006a, 2006b; Stodden et al., 2005). In accord with previous findings (Schmidt & Sherwood, 1982; Sherwood & Schmidt, 1980; Sherwood, Schmidt, & Walter, 1988), variability in force output peaked at 60% of maximum throwing velocity. The finding that, on average, unskilled subjects exhibited less variability than skilled subjects with the exception of 90% and 100% may seem counterintuitive. However, as frequently demonstrated in motor control research, a strategy often used by individuals when confronted with novel tasks is to constrain or “freeze” degrees of freedom (Bernstein, 1967; Whiting, 1984). It is likely that skilled subjects have accumulated more experiences in throwing that have allowed them to explore different strategies for producing the same ball velocity (i.e., differentially modulating force with different segments, exploring different preparatory positional configurations, and differentially manipulating timing of segmental interactions). Thus, they have a greater neuromotor repertoire to successfully perform the task of throwing at one specified velocity (Barrett & Burton, 2002; Langendorfer &
26
Figure 2. Mean radial error (cm) or spatial accuracy as a function of percentage of maximum effort across all subjects.
Impulse Variability Theory and Overarm Throwing 27
Roberton, 2002). However, this ability to choose various coordination patterns at each specified velocity, except for maximal performance, may have promoted more variability at the lower percentages of maximum compared with unskilled subjects. Unskilled subjects may have limited composite coordination solutions to promote velocity at specified speeds. In essence, decreased velocity variability in unskilled subjects, compared to skilled subjects, at most velocity percentages may have resulted from the limited coordination strategies that could be utilized to solve each specific velocity requirement (Langendorfer & Roberton, 2002). The results concerning spatial error are not quite as straightforward. While the trends in velocity variability suggest less variability exists in the accelerative forces and timing between segmental interactions toward the maximal end of the force-velocity continuum, error in the projectile’s terminal spatial location does not seem to follow the same trend. This finding runs counter to postulations of impulse-variability theory suggesting that error in the spatial trajectory of the limb is determined by variability in the muscular forces and torques projecting the limb. However, in the context of the overarm throw where multiple body segments must be coordinated, the spatial path of the projectile can be influenced by a combination of errors in the preparatory spatial orientation of the various segments in space (Chowdhary & Challis, 1999; Stodden et al., 2001) and timing of ball release (Jegede et al., 2005). These sources of error do, indeed, emanate within the movement pattern, but they may operate somewhat independent of the manner in which force is regulated. This reinforces the understanding that the projectile’s spatial error is not exclusively associated with the magnitude of force as proposed by impulse-variability theory. As such, in ballistic, multijoint skills the projectile’s spatial trajectory should be conceptualized as a variable that cannot be explained simply as a function of overall force magnitude. Limited research has addressed error in the projectile’s spatial trajectory during ballistic, multijoint movements (Cauraugh, Gabert, & White, 1990; Van den Tillaar & Ettema, 2003). These two studies, in agreement with the data from this study, do not support a linear speed-accuracy trade-off, as proposed by Fitts’ Law. It is reasonable to assume the variability in preparatory segmental alignments and timing of ball release may have contributed to the variability in spatial error over the entire range of velocities produced. If these parameters were consistent, the spatial accuracy may have followed the inverted-u trajectories associated with variability in ball variability. Further testing of the speed-accuracy trade-off in ballistic, multijoint movements is warranted. In accordance with the recommendations of the impulse-variability theorists, we believe there are practical applications for these results. Decreased variability in throwing velocity at higher percentages of force output demonstrated in this study suggests sacrificing speed for accuracy in ballistic skills may be detrimental for motor skill development, especially in early skill acquisition (Roberton, 1996). The lack of differences in the projectile’s spatial error over the spectrum of force output suggests that maximum projectile velocity should be promoted early in skill acquisition. In essence, if an individual exhibits less variability in force output at near-maximal levels of throwing velocity, practitioners can address preparatory limb configurations to alter spatial error of the projectile. Effecting change in the preparatory positioning of segments is arguably more accessible than manipulating the magnitude forces and torques and timing of segmental interactions that may
28 Urbin, Stodden, Boros, and Shannon
be more variable at submaximal effort. Future research should directly examine variability in kinematic, kinetic, and temporal parameters of ballistic, multijoint movements as a function of overall force output. Given the findings of the current study, it is also necessary to consider the association between fluctuations in preparatory limb alignment and resultant error in the projectile’s spatial trajectory.
Limitations The current study was necessary to identify baseline trends in the variability of force output as a function of percentage of maximum velocity in overarm throwing. However, conclusions from this study are limited in that force production (i.e., kinetics) and the timing of segmental interactions were not directly measured. Conclusions of the current study are also limited in that the subjects’ perception of a spatial accuracy constraint may have increased their emphasis on accuracy. Thus, projectile trajectories may have been influenced by the coupling of demands to achieve both the target velocity and target accuracy. However, the ecological validity of throwing at a target is present in most real-world applications. Examining a wide range of criterion velocities, though it provided a comprehensive scope, promoted potential methodological limitations for assessing spatial error variability, specifically as it relates to unskilled throwers. The limited range of velocities unskilled subjects were able to exhibit caused ball velocities from individual trials to cross into other criterion ranges of percentage maximum with slight fluctuations in throwing velocity (e.g., ≥ 3 mph). This ultimately led to difficulty in qualifying the variability in spatial error according to each specific percentage of maximum velocity. Schmidt and Sherwood (1982) used a bandwidth ± 10% to compare variability in spatial error across different force conditions. This was not an appropriate procedure for the current study due to a crossover in velocities produced at various percentages of maximum. Consequently, two different statistical analyses were necessary.
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