🎾 Variability Of Impact Kinematics¶
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Variability Of Impact Kinematics — tài liệu 7 trang từ thư viện sách tennis.
Chủ đề chính: Forehand, Kinematic
Tóm tắt nội dung (trích từ tài liệu gốc): See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/225748153 Variability of impact kinematics and margin for error in the tennis forehand of advanced players Article in Sports Engineering � January 2005 DOI: 10.1007/BF02844005 CITATIONS READS 19 458 2 authors: John Blackwell Duane V Knudson University of San Francisco Texas State University 21 PUBLICATIONS 513 CITATIONS 189 PUBLICATIONS 2,947 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Qualitative Movement Diagno
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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/225748153
Variability of impact kinematics and margin for error in the tennis forehand
of advanced players
Article in Sports Engineering � January 2005
DOI: 10.1007/BF02844005
CITATIONS READS
19 458
2 authors: John Blackwell
Duane V Knudson University of San Francisco
Texas State University 21 PUBLICATIONS 513 CITATIONS
189 PUBLICATIONS 2,947 CITATIONS
SEE PROFILE
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Variability of impact kinematics and margin for error in
the tennis forehand of advanced players
Duane V. Knudson* and John R. Blackwell
*California State University, Chico
University of San Francisco
Abstract
The kinematics of the racket and ball near impact in tennis forehands were studied to document
typical variation in successful and unsuccessful shots, in order to determine biomechanically mean-
ingful differences in advanced players and confirm models of groundstroke trajectories. Seven
tennis players (six males and one female) were videoed from the side at 180 Hz as they performed
40 forehand drives on an indoor tennis court. Vertical plane kinematics of the racket and ball near
impact were analysed for sub samples of successful and unsuccessful shots for each subject. Most
racket kinematic variables were very consistent (mean CV < 6.3%) for successful shots, so bio
mechanically meaningful differences in angles and velocities of the racket and ball (3� and 2 m s�1)
near impact could be detected between successful and unsuccessful shots. Four subjects tended to
miss long and three subjects missed shots in the net that were reflected in initial ball trajectories.
Mean (SD) initial trajectories for long shots were 9.8� (1.4�), while netted shots were 0.7� (1.1�)
above the horizontal. The initial ball trajectories and margins for error for these subjects were
smaller than those previously reported (Brody, 1987) because players tended to select mean ball tra-
jectories close to one error than another, differing amounts of topspin, or incorrect lift and drag
coefficients for tennis balls had not been published when this model was created. The present data
can be used to confirm if recent models (Cooke et al., 2003; Dignall et al., 2004) more closely match
actual performance by advanced players.
Key words: angle, biomechanics, consistency, error, model, velocity
Introduction a player's stroke. Knudson (1990) reported that within
stroke variation of the angular kinematics of skilled
Research on variability in the sport of tennis has been players differed across the temporal phases of the
limited. Most tennis research only analyses single stroke and increased in higher order kinematic
strokes, assuming consistent movement kinematics of variables. Knowledge of the consistency of biome-
chanical variables in tennis is important because these
Correspondence address: data are used as inputs or for validation in computer
Duane V. Knudson models of the sport.
Department of Kinesiology
California State University, Chico Research was needed on the consistency of the
Chico, CA 95929-0330 kinematics of the racket at impact in tennis. These
Tel: (530) 898-6069 data are needed to determine if the stroke paths to
Fax: (530) 898-4932 impact for various spins reported in the literature
E-mail: dknudson@csuchico.edu (Knudson & Elliott, 2004) are representative, and to
� 2005 isea Sports Engineering (2005) 8, 75�80 75
Variability of impact D.V. Knudson and J.R. Blackwell
improve our understanding of stroke errors and plane (two-dimensional) motion of the racket and ball
margins for error (Brody 1987). The practical impor- near impact. The field of view was about 4 m wide and
tance of research on movement variability relates to was calibrated so the mean error in the digitised width
our understanding of the size of meaningful changes of a tennis ball was less than 5 mm. This would result
in biomechanical variables (Salo & Grimshaw, 1998) in maximum errors in ball velocity calculation of about
and appropriate experimental designs in biomechanics 0.45 m s�1 and maximum angle errors of 1.3�. Three
(Bates et al., 1992; Dufek et al., 1995; Mullineaux et al., points were digitised using Peak Performance
2001). The purpose of this study was to document the Technologies Motus� software, two on the racket head
variability of the vertical plane kinematics of the racket and one the tennis ball. The vertical plane motion of
and ball at impact in the tennis forehand drive of the ball and racket was digitised from fourteen frames
advanced players. A secondary purpose was to see if before impact to eight frames after impact. This
kinematic differences could be detected between suc- interval represents the phase of the stroke with
cessful and unsuccessful strokes, in order to validate minimal racket motion out of the image plane. The
the Brody (1987) model of tennis groundstrokes. midpoint of the racket markers was calculated to
represent the motion of the centre of the racket head.
Materials and methods
Scaled kinematic data were then smoothed with a
Seven right-handed advanced tennis players (six male cubic spline with optimal smoothing selected by the
and one female) volunteered and gave informed program. Five variables were examined: peak resultant
consent to participate in the study. The players were at velocity of the racket prior to impact (VR), the resultant
or above 5.0 rating on the United States Tennis ball velocity six frames after impact (VB), the trajectory
Association National Tennis Rating Program. Two of the racket (TR: angle of racket motion above the
subjects were regionally and nationally ranked juniors, forward horizontal at impact), the inclination of the
with the rest either college or tournament players. The racket face (IR: angle of the racket face to the forward
head of each subject's racket was covered with black horizontal one frame prior to impact), and the trajec-
athletic tape and two white strips of tape were placed tory of the ball (TB: angle of ball motion above the
bilaterally at least 9 cm from the centre of the head. horizontal six frames after impact). The smoothing and
the selection of the frame relative to impact for each
Subjects were instructed to hit their `best topspin variable was selected to limit the effects of signal distor-
forehand drives' off balls fed to them by an investiga- tion by smoothing data through impact (Knudson &
tor stationed in the advantage service box of an indoor Bahamonde, 2001). Descriptive data (mean � SD) for
tennis court. To simulate actual tennis play, player's each variable in successful and unsuccessful shots were
rallied four series of ten forehands, aiming their calculated for each subject. Within-subject comparisons
strokes down the centre of the court at the opposite of mean data from successful and unsuccessful shots
centre mark. New tennis balls were thrown to the were based on 95% confidence intervals calculated
subjects by the same investigator so that consistent from the successful shots.
ball bounce, placement and speeds (7.6 � 0.8 m s�1)
before racket impact would allow the player's racket to Results
intercept the ball in the vertical area above the centre
service line. Stroke success was coded by another Descriptive data for the successful shots are listed in
investigator based on vertical plane accuracy of the Table 1. Three players did not have five errors of one
ball: hitting the net, landing in the court, or landing type, so mean error data for these players were based on
beyond the baseline. Ten trials were selected for smaller samples (3�4) of strokes. Three of the five
kinematic analysis, the first five successful shots and impact variables showed very high consistency. The
five of the modal error type for that subject. mean (SD) coefficients of variation for racket inclina-
tion (IR), the resultant velocities of the racket before
High-speed (180 Hz) videography (JC Labs impact (VR) and the ball after impact (VB), were 3.3
HSC180, Mountain View, CA) was collected from a (1.3), 6.3 (1.8), and 5.7 (1.5) per cent, respectively. This
lateral view of all strokes to document the vertical
76 Sports Engineering (2005) 8, 75�80 � 2005 isea
D.V. Knudson and J.R. Blackwell Variability of impact
was in agreement with the low (< 6.4%) variability of The other three players tended to miss forehands
forehand angular kinematics reported in a previous hitting the net (Table 3) and all three had significantly
study (Knudson, 1990). Racket trajectory before impact lower ball trajectories (3.0 to 4.4 degrees) compared to
(TR) and ball trajectory (TB) after impact had nominally their successful shots. These players stroked the ball
higher variability, with coefficients of variation of 12.5 nearly horizontal (4.3 � 0.3 degrees) in successful
(3.2) and 23.4 (7.8) per cent, respectively. shots and shots into the net (0.7 � 0.6 degrees), so they
had very little margin for error in clearing the net.
Four players tended to miss shots long (Table 2) None of the other impact variables were significantly
with three of these players showing significant different from values measured in successful shots.
(P < 0.05) differences in some kinematic variables
from their successful shots.
Table 1 Mean impact kinematics of successful forehands
VR (m s�1) TR (deg) IR (deg) VB (m s�1) TB (deg)
M SD M SD M SD M SD M SD
S1 25.8 1.4 24.9 4.3 83.2 4.9 29.8 1.8 4.3 1.1
30.2 3.1 84.0 3.2 28.3 1.7 9.6 1.5
S2 24.1 0.8 26.5 4.2 84.4 3.1 32.7 1.6 8.2 1.1
31.2 3.3 86.8 2.6 28.8 1.0 8.6 1.6
S3 25.8 2.0 28.4 3.1 86.2 2.6 28.9 1.4 7.1 2.1
28.5 4.0 87.7 1.9 27.9 1.7 4.6 1.2
S4 22.4 1.4 22.7 2.0 88.1 1.6 31.4 2.6 4.0 1.4
S5 24.3 1.3
S6 21.8 1.7
S7 25.9 2.2
Mean 24.3 1.5 27.5 3.4 85.8 2.8 29.7 1.7 6.6 1.4
Variables are the peak resultant velocity of the racket before impact (VR), the trajectory of the racket at impact (TR), the inclination
of the racket face at impact (IR), the resultant velocity of the ball after impact (VB), and the trajectory of the ball after impact (TB).
Table 2 Mean impact kinematics of forehands missed long
VR (m s�1) TR (deg) IR (deg) VB (m s�1) TB (deg)
M SD M SD M SD M SD M SD
S2 23.0 1.0 32.9 8.8 81.4 7.9 29.5 1.8 11.9* 2.4
30.2 2.2 86.9 3.0 36.0 2.1 8.9 1.2
S3 26.1 1.6 27.4 0.8 88.6 1.3 35.2* 2.3 8.2 0.8
28.9 4.2 82.8* 7.8 28.5 3.0 10.0* 1.0
S4 26.8* 1.3
S5 21.7* 1.7
Mean 24.4 1.4 29.9 4.0 84.9 5.0 32.3 2.3 9.8 1.4
*Significantly (P < 0.05) different from successful shots by this subject.
Table 3 Mean impact kinematics of forehands into the net
VR (m s�1) TR (deg) IR (deg) VB (m s�1) TB (deg)
M SD M SD M SD M SD M SD
S1 25.3 1.3 30.1 3.9 86.0 2.2 28.9 3.0 1.3* 1.5
31.8 3.9 86.1 4.0 28.2 2.5 0.2* 1.2
S6 22.4 1.4 23.6 4.0 83.8* 8.7 28.7 6.0 0.5* 0.5
S7 25.1 2.2
Mean 24.3 1.6 28.5 3.9 85.3 5.0 28.6 3.8 0.7 1.1
*Significantly (P < 0.05) different from successful shots by this subject.
� 2005 isea Sports Engineering (2005) 8, 75�80 77
Variability of impact D.V. Knudson and J.R. Blackwell
Discussion It is also possible that the lack of agreement in initial
ball trajectories between the present data and the Brody
Values for all five dependent variables studied were model could be related to experimental errors, less
consistent with previous research on tennis forehands. topspin used by the players than assumed in the model,
The mean VR prior to impact in successful strokes or incorrect lift and drag coefficients assumed by the
(24.3 � 1.5 m s�1) was similar to previous studies of computer model. Errors in ball position and velocity
advanced (19�23 m s�1) subjects (Elliott et al., 1989; are not likely large enough to account for differences
Knudson & Bahamonde, 1999; Takahashi et al., 1996), (3� and 2 m s�1) that turned out to be biomechanically
although true racket speed at impact is likely to be ten significant. Unfortunately, the sampling rate used in
to twenty per cent higher since smoothing through this study would not allow for accurate measurement of
impact distorts the data near impact (Knudson & ball rotation. Aerodynamic coefficients for tennis balls
Bahamonde, 2001). The racket face was very close to have only recently been reported (Goodwill et al., 2004;
vertical with a mean IR of 85.7 � 2.8 degrees. Previous Metha & Pallis, 2001) and are larger than for smooth
studies have also shown that the racket face near sphere values used by Brody. Recent computer models
impact in groundstrokes is usually very close (< 10�) to using these new coefficients have been reported (Cooke
vertical (Knudson & Elliott, 2004). The mean TR at et al., 2003; Dignall et al., 2004), but the authors have
impact was 27.5 � 3.4 degrees above the horizontal for not published monograms that can be compared to the
successful shots. This racket path was similar to upper data from this study.
range values reported for flat groundstrokes and
slightly less (35�45 degrees) than for topspin strokes The players in the current study also had smaller
(Knudson & Elliott, 2004). It is possible that these margins for error than predicted by computer models
subjects used lower range racket trajectories because because they tended to create strokes that are not in
the pre-impact ball speeds and spin were moderate the middle of the window of success. For example, the
and did not require a very steep racket path to reverse mean TB for the players that missed long
ball rotation. (9.8 � 1.4 degrees) was not outside Brody's theoretical
window of success, but it was very close to the mean
The initial ball trajectories (TB) in the present study trajectory of their successful shots (8.4 � 1.0 degrees).
(2.4 to 12.1 degrees) were slightly lower than those for
similar strokes predicted by the computer model Most of the impact kinematic variables (IR, VR and
(8�16 degrees) reported by Brody (1987). Brody VB) of successful shots in these advanced players were
presented graphs of computer simulations that show highly consistent (CV < 6.3%). This was in agreement
that successful baseline strokes with topspin with a previous study of multiple forehands of advanced
(32 rev s�1) and ball speed (24.3 m s�1) similar to the players (Knudson & Bahamonde, 1999). Based on the
present study would have an 8� window (8�16 degrees variability in the present data it is likely that meaningful
above the horizontal) for shot success. The present biomechanical differences in impact velocities and
data indicate a range for topspin forehand success angles of the ball and racket in tennis forehands can be
slightly below (2.4�12.1 degrees) the simulations, detected at about 2 m s�1 and 3�, respectively.
which could be due to differences in the amount of
topspin used in the strokes. The mean impact position The low variability of impact kinematic variables in
on the court in this study was nearly identical to the the present study allowed for the detection of differ-
values assumed by the Brody model. Mean (SD) ences between successful and unsuccessful strokes.
height and distance behind the baseline that the ball The mean TB (Table 1) for successful shots was
was impacted for successful shots by these subjects was bimodal, as three subjects had low (4.3 � 0.3 degrees)
0.729 (0.076) m and 0.038 (0.246) m, respectively. It is ball trajectories and four subjects had higher
logical that lower ball trajectories would be used, since (8.4 � 1.0 degrees) ball trajectories. This corre-
these players used a flatter racket path and higher sponded well with ten statistically significant (p < 0.05)
resultant ball velocities than reported by Elliott et al. differences in four impact variables in six of the seven
(1989) for topspin forehands. players (Tables 2 and 3). Only racket trajectory prior
to impact (TR) had no significant differences between
successful and unsuccessful forehands.
78 Sports Engineering (2005) 8, 75�80 � 2005 isea
D.V. Knudson and J.R. Blackwell Variability of impact
Forehand stroke success depends on the position of between a ball that landed successfully in the court and
the ball at impact, and the speed, spin and angle of ball one that did not land in the court were errors in initial
projection. The data also indicated that there could be ball trajectory of only 2�4 degrees. These players also
different combinations of these impact variables that tended to create ball trajectories closer to one error
result in successful or unsuccessful strokes. For than another and had different combinations of
example, in the players who tended to miss strokes impact variables that tended to result in stroke errors.
long, one (subject 2) had significantly higher TB (2.3�), These players had smaller margins for error than have
while another (subject 4) had significantly higher VR been predicted by the Brody (1987) model. This dis-
(4.4 m s�1) and VB (6.4 m s�1) in missing long. crepancy may be due to differences in topspin or the
Interestingly, subject five had significant differences in lack of accurate drag and lift coefficients for tennis
VR (�2.6 m s�1), IR (�3.4�), and TB (2.9�) in shots missed balls at the time Brody's model was developed. The
long. Lower values of VR and IR would tend to result in current data can be used to help validate new models
lower initial ball trajectories, but TB was significantly of tennis groundstrokes using recently published
higher for this player. It is unknown how these tennis ball aerodynamic data (Goodwill et al., 2004;
opposing factors combined to make this player's shots Metha & Pallis, 2001).
unsuccessful, but it is possible that more off-centre
impact locations on the strings could have decreased References
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