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Journal of Sports Sciences
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Perceiving the affordance of string tension for power
strokes in badminton: Expertise allows effective use of
all string tensions
Qin Zhu a
a Division of Kinesiology and Health, University of Wyoming , Laramie , WY , 82071 , USA
Published online: 18 Feb 2013.
To cite this article: Qin Zhu (2013) Perceiving the affordance of string tension for power strokes in badminton: Expertise
allows effective use of all string tensions, Journal of Sports Sciences, 31:11, 1187-1196, DOI: 10.1080/02640414.2013.771818
To link to this article: http://dx.doi.org/10.1080/02640414.2013.771818
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Perceiving the affordance of string tension for power strokes in
badminton: Expertise allows effective use of all string tensions
QIN ZHU
Division of Kinesiology and Health, University of Wyoming, Laramie, WY 82071, USA
(Accepted 28 January 2013)
Abstract
Affordances mean opportunities for action. These affordances are important for sports performance and relevant to the
abilities developed by skilled athletes. In racquet sports such as badminton, different players prefer widely different string
tension because it is believed to provide opportunities for effective strokes. The current study examined whether badminton
players can perceive the affordance of string tension for power strokes and whether the perception of affordance itself
changed as a function of skill level. The results showed that string tension constrained the striking performance of both
novice and recreational players, but not of expert players. When perceptual capability was assessed, perceptual mode did not
affect perception of the optimal string tension. Skilled players successfully perceived the affordance of string tension, but
only experts were concerned about saving energy. Our findings demonstrated that perception of the affordance of string
tension in badminton was determined by action abilities. Furthermore, experts could adjust the action to maintain a
superior level of performance based on the perception of affordance.
Keywords: affordances, constraints, motor expertise, badminton
Introduction
A general belief held by racquet sports players is that
playing performance is enhanced if the “right”string
tension is chosen for their racquets. Often, we hear
that elite tennis players prefer a particular string
tension that has to be frequently checked during a
match. In competitive badminton, it is often
reported that experienced players prefer widely dif-
ferent string tension for their performance, and
novice players request recommendations for ideal
string tension when they first have their racquets
strung. It remains unclear, however, what effect
string tension has on performance by players at var-
ious skill levels.
Scientists have investigated the effect of string
tension in tennis. Using the rigid clamping method,
Elliott (1982) reported that a lower string tension
resulted in a higher rebound velocity if the racquet
was flexible. Bower and Sinclair (1999) found that
rebound angle was influenced by string tension dur-
ing an oblique impact. While a lower string tension
produced greater rebound impulse (thus a greater
velocity), the rebound angle was closer to normal. A
change of rebound angle would directly affect stroke
accuracy. Brody and Knudson (2000) modelled the
dynamics of impact to determine the effect of string
tension on stroke accuracy. According to their
model, when string tension is lowered, the effect of
a longer dwell time together with significant racquet
rotation in recoil leads to a greater deviation
between ball incident (the angle at which the ball
impacts the racquet string bed) and rebound angle,
thus making it difficult to control a shot. These
results show that changes in string tension produce
a speed-accuracy trade-off, such that reducing
string tension helps to increase ball speed at the
cost of decreasing accuracy.
The above conclusion is limited by the fact that it
was based on testing only the dynamics of impact
without including analysis or testing of human fac-
tors. In none of these studies did players interact
with a strung racquet and ball. The question is
whether the effects of string tension found in the
laboratory would be seen in the field during play.
Bower and Cross (2005) investigated this using a
ball projection machine. Tennis players at com-
petitive level were asked to return balls with three
differently strung racquets. Rebound speed and
accuracy were recorded. The results were in line
with those reported in the previous laboratory
Correspondence: Qin Zhu, Division of Kinesiology and Health, University of Wyoming, Dept. 3196, 1000 E. University Ave, Laramie, WY 82071, USA.
E-mail: qzhu1@uwyo.edu
Journal of Sports Sciences, 2013
Vol. 31, No. 11, 1187–1196, http://dx.doi.org/10.1080/02640414.2013.771818
© 2013 Taylor & Francis
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studies, that is, low string tensions produced greater
rebound speeds, but string tension seemed to
affect ball placement and thus accuracy. In a subse-
quent study performed by the same researchers
(Bower & Cross, 2008), elite tennis players were
tested using the same procedure, but the results
were conflicting. High string tension, instead of low
string tension, produced significantly higher
rebound speed, and ball placement did not appear
to be related to string tension. The contradictory
findings from these two studies suggest that the
expertise of the players might play an important
role in determining the effects of string tension on
performance. Experts might be better able to adapt
to the changing string tension to maintain superior
performance. Bower and Cross (2003, 2008) also
tested the tennis players’sensitivity to changes of
string tension and reported that elite tennis players
seemed to be insensitive to the changing string ten-
sions. However, the limited ability demonstrated by
elite tennis players in detecting changes of string
tension might be attributed to the limited impact of
string tension on their playing performance,
although it remains unclear why string tension fails
to affect this performance. The question that arises
naturally is whether expert players can detect string
tension and use this perception to adjust their stroke
to yield consistent superior performance.
The study of affordances provides a new framework
for investigation of string tension effects. Affordances
are environmental properties of objects and events in
relation to an animal’s action capabilities relevant to
performing specific tasks (Gibson, 1979/1986;
Turvey, 1992). People are capable of perceiving affor-
dances such as whether or not objects can be grasped
(Newell, Scully, Tenenbaum, & Hardiman, 1989),
reached (Mark et al., 1997), or climbed (Mark,
1987) given the scale of the observer and his or her
relevant limbs (hands, arms and legs, respectively). In
sport, the perception and use of affordances is critical
to successful performance. Oudejans, Michaels,
Bakker, and Dolne (1996) investigated the catch-abil-
ity of a flying ball and showed that movement, such as
initiating approach to the future landing position, was
required to perceive the affordance. Similarly, Hove,
Riley and Shockley (2006) showed that hockey
players were able to select the optimal hockey stick
for power and precision tasks by wielding differently
weighted sticks. Carello, Thuot, Anderson, and
Turvey (1999) found that both novice and expert
tennis players could judge the location of the “sweet
spot”in a tennis racquet. As an essential property of
racquets, string tension may provide opportunities for
effective and successful play. In this case, however,
the role of this property may depend on the level of
skill of the player who is required to judge its
affordance.
Perception of affordances entails a relation
between the environmental properties and actor’s
action capabilities. As pointed out by Fajen, Riley,
and Turvey (2008), perception of affordances could
be dynamic due to changes occurring both in the
environment and the actor. Actors can change in a
number of ways (e.g. growth and development,
injury, fatigue), but perhaps the most relevant to
action capabilities in sport is the acquisition of effec-
tive skills. Such changes in an actor’s action system
will change the relation between environmental
properties and the actor’s action capabilities, which
determines an affordance. An actor’s perceptions
have been found to adapt in the face of changes in
these relations. For instance, Mark (1987) investi-
gated the perception of maximum seat height when
the sitters were asked to wear blocks to their feet,
thus changing their relation to useable seat heights.
It was found that the observers exhibited progressive
adaption until judgments were again accurate, which
occurred without experience of sitting while wearing
the block. Similarly, Bingham, Schmidt, and
Rosenblum (1989) had found that throwers could
perceive and select objects of optimal weight for
throwing to a maximum distance by hefting different
hand held objects. However, Zhu and Bingham
(2010) wondered whether this ability to perceive
throwing affordance had to be learned through
acquisition of long distance throwing skills.
Unskilled throwers were unable to select optimal
objects for throwing, but after a month of practice
and acquisition of long distance throwing ability,
they were able to do this task. The objects they
selected at the end of the study were different from
the ones with which they had trained, but still accu-
rate. This study showed that the ability to perceive
affordances is coupled with the ability to perform the
relevant actions.
Using the framework of affordances, we now
investigate the perception and use of string tension
in badminton. Badminton is considered to be the
world’s fastest racquet sport. According to USA
Badminton (Colorado Springs, Colorado, USA),
the recorded speed of a shuttlecock immediately
after impact could reach 206 miles per hour, that
is, 1.6 times faster than the fastest ball in tennis.
Although a relatively thinner string is used in bad-
minton, allowing for more rebound speed during
impact, a badminton court is significantly smaller
in dimension than a tennis court. To keep shots
within boundary while producing maximum speed,
players select string tension to allow for accuracy
as well as speed. This demand on string tension
in badminton makes it an appropriate focus for
study.
The current study is aimed to answer two
research questions. First, does the optimal string
1188 Q. Zhu
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tension exist for power strokes produced by players
at different levels of expertise? It was hypothesised
that different string tensions would result in differ-
ent shuttlecock speeds after impact, and an optimal
string tension should produce the greatest shuttle-
cock speed after impact. However, the expertise of
the player was expected to affect how different
string tensions were used. Hence, different string
tensions might be found to be optimal depending
on the player’s level of expertise. Second, could
players at different levels of expertise perceive the
affordance of string tension for power strokes? It
was hypothesised that the affordance would be bet-
ter perceived by players with greater expertise,
assuming that this would be part of their expertise
(the perceptual expertise). However, is there a sen-
sory mode that is optimal for perceiving this affor-
dance? Badminton players judge string tension in
various ways: by pressing the string bed directly, by
listening to the sound resulting from hitting the
string bed with heel of the hand, or by watching a
shuttlecock bouncing off a racquet, and finally, by
simply hitting several shots. According to Shaw and
Bransford (1977), action-dependent properties
should be specified equally well in optic, acoustic
and haptic information. Hence, affordances should
be perceived equally well using different sensory
modalities. Warren, Kim, and Husney (1987)
showed that the elasticity of a ball used for a bounce
pass could be perceived equally well using visual
and auditory information. Similarly, Fitzpatrick,
Carello, Schmidt, and Corey (1994) showed that
whether a slanted surface would support upright
stance could be perceived both visually and hapti-
cally. Both studies implied that the affordance of
string tension would be equally well perceived in
different perceptual modes.
Methods
Participants
Twelve adult participants were recruited on the
campus of the University of Wyoming (UW). They
were selected to represent three skill levels in play-
ing badminton: expert, recreational and novice.
To be considered as expert players, participants
were required to have played badminton actively
and competitively within the last 5 years, and accu-
mulated approximately 10,000 hours of deliberate
practice in their lifetime (Ericsson, Krampe, &
Tesch-Römer, 1993). To be considered as recrea-
tional players, participants were required to have
played badminton or other racquet sports occasion-
ally, but only for fun. Novice players may have
played in a PE class before, but not have played
otherwise on any occasion. All participants were
interviewed about their previous experience of play-
ing badminton to determine their level of skill. Four
expert players (3 male and 1 female) and four
recreational players (3 male and 1 female) were
recruited from the UW Badminton Club. Four
novice players (1 male and 3 female) were recruited
from the regular student population. Participants
were right-handed, aged between 20 years and 40
years, and free of any motor or sensory deficit.
Informed consent was obtained as governed by the
Institutional Review Board (IRB) at UW.
Apparatus
Using a stringing machine (Eagnas Combo 910,
Gardena, CA), eight badminton racquets of the
same model (Yonex Nanospeed 9000, Torrance,
CA) were strung with the same type of string
(Yonex BG 65) to achieve tensions of 16 lb, 18 lb,
20 lb, 22 lb, 24 lb, 26 lb, 28 lb, and 30 lb. The
pulling tension for the main string was set at the
target tension level, and that for the cross string
was increased by 2 lb.
Since the resulting string tension typically requires
time to settle after stringing, all strung racquets were
measured and monitored for change of tension after
the stringing. The actual string tension on each rac-
quet was determined by measuring the vibration
frequency of the strings (Cross & Bower, 2001;
Röttig, 2010). The experimenter swung the racquet
rapidly to hit the heel of his hand with the string bed.
The resulting sound of impact was recorded directly
onto a computer through a microphone set right
next to the collision point. The fundamental fre-
quency was determined using audio analysis soft-
ware (Audacity). This frequency was then used in
the following the equation to determine the actual
string tension:
S¼8:82 Aμð0:988fÞ2
9:81 107(1)
where
A= area of the racquet head (to wincm
2
)
µ = mass-density of the strings (densitg · m
−1
)
f= fundamental frequency of the strings in Hz
S= string tension in lbs.
It was found that string tensions on each racquet
dropped significantly after stringing by about 6 lb,
but these changes stopped after a month, similar to
the findings of Cross and Bower (2001). The mea-
sured tensions after a month were compared to the
intended tensions, and a significant correlation was
found (F(1, 7) = 1688.7, P< 0.001, R
2
= 0.99),
showing that the tension intervals were preserved
despite the significant drop in the average tension.
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Once the string tensions had stabilised, the corre-
sponding impact sounds were saved and edited as
auditory stimuli for later judgment tests. Eight sound
tracks were saved for the eight tension levels, respec-
tively. Each sound track was then edited to be five
repetitions of the same impact sound evenly spaced
in five seconds.
The string tensions were also recorded visually.
Each racquet was fixed on a stringing machine with
its string bed facing upwards. A small reflective ball
(2 inch in diameter) was projected vertically from
above the string bed from the same height at the
same angle using a commercially available ball gun
(Nerf Atom Balster). The motion of the ball before
and after impact was recorded at 250 frames per
second using a high speed camera (SportsCam 500
by Fastec Imaging, San Diego, CA) that was oriented
perpendicular to the direction of motion. Eight video
clips were made for the eight tensions, respectively.
Each clip was then edited to be five seconds long and
only contain the visual display of the bouncing ball
event played at a rate of 30 frames per second.
The same fast speed camera (SportsCam) was
used to record power strokes performed by partici-
pants using the various strung racquets. The camera
was set on a tripod perpendicular to the primary
plane of motion at a distance of five metres. The
distance allowed maximum spatial resolution of the
entire range of motion. Compatible software
(MaxTRAQ 2D) was used to control the camera
and record the motions at 250 frames per second
with a shutter speed of 1/2500 second. A black cur-
tain was behind the participant who was illuminated
by two studio lights (Q60SG/1200-Watt by Smith
Victor, Bartlett, IL). Using additional software
(MaxMATE), two-dimensional (2-D) motion analy-
sis was performed to recover speed and direction of
motion of the shuttlecock after impact using a third
order low-pass filter with a cut-off frequency of
15 Hz (Winter, 1990; Yu, 1988).
Procedure
First, the power stroke was described to participants
as the stroke that will result in the greatest speed of
the shuttlecock after impact. Then, participants were
informed that the task was to determine the differ-
ence between string tensions on racquets, and select
the tension that would allow for the most powerful
stroke. They were encouraged to judge based on
their own intuitive feeling without any subjective
reasoning. Participants were subject to a perceptual
judgment test first, in which they were asked to judge
optimal string tension in each of three perceptual
modes, and then the performance test in which
they were asked to perform power strokes using
racquets with the various string tensions. After the
performance test, participants were asked to judge
the optimal string tension again.
Pre-performance judgments. The eight string tensions
were presented to participants in visual, auditory and
haptic modes. The order of the perceptual modes
was randomised. In the visual mode, participants
watched eight silent video clips of a ball bounced
off the respective string beds. In the auditory mode,
participants heard eight sound tracks of the string
beds being hit by the experimenter’s hand. In the
haptic mode, participants pressed the string bed of
each racquet using their fingers with eyes closed and
ears plugged. In each condition, tensions were initi-
ally presented either in an increasing or decreasing
order. These orders were counterbalanced across
participants. Participants were allowed then to com-
pare different string tensions as many times as they
wanted to select the best three string tensions in
order, namely, the first, second and third preferred
tensions.
Performance test. Perceptual judgments were followed
by performance tests. Participants were encouraged
to warm up their shoulders and arms before testing.
Then, they were asked to swing a racquet three times
at maximum speed. Next, participants were asked to
perform power strokes using racquets strung with
the different tensions. In typical game play, players
are required to strike a flying shuttlecock during
movement, however, the ability to locate and move
underneath the shuttlecock to prepare for striking
may confound the ability to use different string ten-
sions to produce power strokes. Hence, we modified
the striking condition by asking players to strike a
static suspended shuttlecock above their head.
A feather shuttlecock was hung from the ceiling
through a nylon fishing line that had one end fixed
to the ceiling and the other end folded to hook the
skirt of the shuttlecock. The shuttlecock was sus-
pended obliquely with its cork head going to be hit
by the racquet first. Participants were asked to hold
the racquet as comfortably as they would, and fully
extend their arm upward so that they could reach
high above their head with the racquet. Then, the
suspended shuttlecock was adjusted to the partici-
pant’s preferred striking height at which the string
bed would make full contact with the shuttlecock
during impact. Participants swung each racquet
with maximum power to strike the shuttlecock so
that it would detach from the fishing line, launch
and land in the matted area on the front wall,
which was located approximately 3 m away from
where the shuttlecock was suspended. They were
asked to do this three times using each racquet,
yielding a total of 24 trials. All participants suc-
ceeded in striking the shuttlecock to hit the matted
1190 Q. Zhu
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area. To prevent fatigue, a two minute break was
provided between trials. String tensions were tested
either in an increasing or decreasing order of ten-
sion, counterbalanced across participants, but the
order was different from that in the perceptual judg-
ment test. All trials were recorded using the high
speed camera at a speed of 250 frames per second.
Post-performance judgments. Immediately after the
performance test, participants were asked to judge
preferred string tension again (selecting their top
three choices again in order). They were told that
their judgment should be based on their immediate
feeling about each tension during and after produ-
cing power strokes. Participants’preferred tensions
were recorded to compare with those judged
previously.
Results
Effect of string tension on striking performance
The effect of string tension on striking performance
was examined as a function of expertise. As shown in
Figure 1, the mean maximum speeds varied with the
string tension, but in different ways for different skill
levels: they decreased for novice players, increased
for recreational players, but remained steady for
expert players, indicating that the effect of string
tension on power strokes depended on the player’s
level of expertise. Speeds also varied as would be
expected with expertise: they were greatest for
experts, and least for novice players.
A 3-way (skill by tension by trial) mixed design
analysis of variance (ANOVA) yielded a main effect
for skill (F(2, 9) = 21.45, P< 0.001, η
2
= 0.83).
A Tukey post-hoc test showed that expert players
generated a significantly higher (P< 0.05) maximum
speed (M= 62.0 ± 4.5 m · s
−1
) than recreational
players (M= 45.8 ± 8.2 m · s
−1
), or novice players
(M= 34.3 ± 6.7 m · s
−1
). Because a significant
interaction was also found between skill and tension
(F(14, 63) = 2.90, P< 0.01, η
2
= 0.80), a simple
main effect analysis was performed to determine
the effect of tension within each skill level. Tension
was significant for novice (F(7, 189) = 2.12,
P< 0.05, η
2
= 0.07) and recreational players
(F(7, 189) = 2.55, P< 0.05, η
2
= 0.09), but not
for expert players (F(7, 189) = 1.26, P> 0.1). A
Tukey-B post-hoc test was followed to find out the
tension corresponding to the speed that was signifi-
cantly higher than others, namely, the optimal ten-
sion. Among the mean speeds produced by novice or
recreational players using all tensions, a peak mean
speed can be identified. This peak mean speed was
compared to other speeds until the significant differ-
ence was found. It was revealed that tensions of 16,
18, and 20 lbs corresponded to a speed significantly
higher than those produced by other tensions for
novice players, and tensions of 24, 26 and 28 lbs
demonstrated the same for recreational players
(P< 0.05). Thus, tensions as low as 16 lb were
optimal for novice players, while tensions as high as
28 lb were optimal for recreational players, and
expert players were able to produce equally fast
strokes using all string tensions. A significant inter-
action between skill, tension and trial was also found
(F(28, 126) = 1.60, P< 0.05, η
2
= 0.26). The
simple main effect analysis was performed to evalu-
ate the trial effect within each skill level, and the
results indicated that a trial effect was significant
only for recreational players (F(2, 144) = 17.11,
P< 0.001, η
2
= 0.19), because they generated sig-
nificantly lower speeds in their third round, suggest-
ing that they might get fatigued in performing the
final trial of the power stroke.
Perceptual judgment of the optimal string tension
Given the performance results showing optimal
string tensions for recreational and novice players,
but not for experts, the next question was whether
those players would judge the respective tensions
as optimal when the string tensions were presented
to them in different sensory modes? To provide
better resolution along this continuous dimension
given the discrete choices, the mean preferred ten-
sion was calculated in each condition by multiply-
ing the preferred tension by 0.5, the second
preferredby0.33,andthethirdby0.17,and
Figure 1. Mean maximum shuttlecock speed after impact as a
function of string tension and skill level. Novice players (filled
squares), recreational players (filled triangles), and expert players
(filled circles). Error bars are standard errors.
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then summing them up. These calculated mean
preferred tensions were then used as a dependent
measure to examine effects of judgment type and
motor expertise on judging the best tension for the
power stroke.
A 2-way (skill by judgment type) mixed design
ANOVA showed a significant effect for skill
(F(2, 9) = 11.81, P< 0.01, η
2
= 0.72). As revealed
by a post-hoc Tukey test, novice players selected a
significantly lower (P< 0.05) tension (M= 22.5
± 3.2 lb) than expert (M= 25.3 ± 2.8 lb) and
recreational (M= 26.5 ± 2.6 lb) players, with no
difference between the last two. These judgments
were fairly reasonable for the novice and recreational
players, but not for the experts, because the experts
failed to exhibit an optimal string tension in their
performance data, but nevertheless, they appeared
to exhibit preferences for a higher string tension.
There was no main effect of judgment type
(F(3, 27) = 0.27, P> 0.5), indicating that the same
tensions were selected before performing the power
strokes regardless of the perceptual mode (vision,audi-
tion, or haptic), as well as after players had tried strik-
ing with all of the tensions. Coefficients of variation
(CV) were used to assess the variability of these judg-
ments. As seen in Table I, novice players were more
variable than skilled players in selecting an optimal
tension, and judgments using the haptic mode were
more variable than using other modes. This latter
result implied that pressing on the string bed to judge
the optimal tension was challenging for all players.
Furthermore, as shown in Table I, there were some
variations among players of different skill levels. The
experts were most variable in judgments made after
performing power strokes. This result indicated that
their preference for higher tension became less reliable
after they had actually used string tensions to hit
shuttlecocks.
Perceiving the affordance of string tension
Two more analyses were performed to better deter-
mine whether the affordance of string tension was
perceived accurately. First, participants’perfor-
mance data was weighted by their judgment data as
follows. For each participant, the mean maximum
speeds of the shuttlecock after impact can be found
for each string tension. These mean maximum
speeds could be weighted by the participant’s
choices, that is, the speed corresponding to the
most preferred tension was multiplied by 0.5, that
corresponding to the second preferred tension by
0.33, and that to the third by 0.17 before they were
summed to yield a weighted average speed. For
those speeds corresponding to the discarded ten-
sions, an average speed was computed by excluding
the highest and the lowest scores to avoid possible
ceiling and floor effects. Thus, two sets of mean
speed scores were created: one corresponded to the
selected tensions, and the other to the discarded
tensions. An ANOVA was performed to examine
choice and its potential interaction with skill level
and judgment type. If we found that the speed cor-
responding to the selected tensions was higher than
that corresponding to the discarded tensions, this
would suggest that players were able to perceive the
affordance of string tension. We found that the
weighted mean maximum speeds were consistently
higher than those for the discarded tensions only for
recreational players. A 3-way (skill by judgment type
by choice) mixed-design ANOVA showed a signifi-
cant effect for skill (F(2, 9) = 21.91, P< 0.001,
η
2
= 0.83, the same as found in analysis of perfor-
mance data), and a marginal effect for the skill by
choice interaction (F(2, 9) = 4.15, P= 0.05,
η
2
= 0.48). Because we already found that higher
speeds corresponded to higher skill level, and that
the type of judgment did not affect selection of the
optimal tension, post-hoc tests were performed only
to investigate the skill by choice interaction. As
revealed by simple main effect analysis, the choice
effect was only significant for recreational players
(F(1, 36) = 7.91, P< 0.01, η
2
= 0.18), suggesting
that only recreational players were accurate in select-
ing the optimal tension for producing a power
stroke.
To confirm this finding, another analysis was per-
formed. This analysis was used previously by Zhu
and Bingham (2008, 2010). For each participant, all
tensions were weighted by a participant’s mean pre-
ferred tension (actual tension/mean preferred ten-
sion), and all speeds were weighted by the peak
Table I. Coefficient of variation (CV) of judged tensions preferred for power stroke.
Judgment Type Expert Recreational Novice Mean
Audio 0.05 0.06 0.11 0.07
Video 0.06 0.16 0.06 0.09
Haptic 0.13 0.10 0.16 0.13*
After-Hitting 0.16 0.07 0.09 0.11
Mean 0.11 0.09 0.14*
Note: Asterisk represents the highest mean CV.
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mean maximum speed that was produced by the
participant (actual speed/peak mean maximum
speed). Then, the weighted speeds were plotted
against the weighted tensions. If judgments of the
affordance were correct, then the plot should exhibit
a peak at the value of 1 on the axis of weighted
tension (that is, where actual tension = mean pre-
ferred tension) and this peak should exhibit a value
of 1 on the axis of weighted speed (that is, actual
speed = peak mean maximum speed). This expecta-
tion could be evaluated by fitting a quadratic func-
tion to the combined data for players at each skill
level. However, given the pattern for speed data
exhibited in Figure 1, this analysis was expected to
work only for the recreational players. As seen in
Figure 2, for novice players, speeds peaked at the
lowest level of string tension. For expert players,
speeds exhibited no significant variation across dif-
ferent string tensions. Thus, good quadratic fits
could not be expected in either case. The analysis
only worked for recreational players. The regression
analysis only yielded a significant (P< 0.05 or bet-
ter) quadratic term for the recreational players
(R
2
= 0.21, F(2, 127) = 16.56, P< 0.001,
Y=–0.23X
2
+ 0.51X + 0.68). The X can be solved
by taking the derivative of this function and then
setting the derivative as 0: X= 1.11. Thus, the
maximum occurred close to 1 on the weighted ten-
sion axis. The function evaluated at this value for X
was Y= 0.96, suggesting that the selected tension
did yield the maximum speed.
Discussion
Anecdotally, string tension is believed to affect play-
ing performance in racquet sports. Although the
string tension effect has been investigated in tennis,
little attention has been paid to motor expertise in
determining the effect. The current study investi-
gated the string tension effect in badminton as a
function of different levels of expertise within the
framework of affordances.
Our results and analyses revealed that recreational
players were sensitive to the affordance of string
tension. They selected a tension (≈26 lbs) that
yielded a maximally effective power stroke for
them, that is, a stroke that yielded the peak max-
imum speed. Novice players selected a tension
(≈22 lbs) that was greater than the one that allowed
them to generate the greatest maximum speed
(≈16 lbs), although they did select a lower tension
than did either recreational or expert players.
Furthermore, novice players exhibited greater varia-
bility in their choices as might be expected given
their level of skill. Finally, expert players reliably
selected a higher tension (≈25 lbs) close to that
preferred by recreational players, despite the fact
that this tension failed to be the only one to yield
the best performance. The experts generated equiva-
lent maximum speeds using all string tensions.
These speeds were greater than those produced by
non-expert players as expected. Thus, according to
these analyses, it seemed, rather paradoxically, that
expert players were not expert in perceiving the
Figure 2. Quadratic regression of weighted tension on weighted speed separated by skill level. The vertical line refers to the condition when
actual tension is equal to the mean preferred tension. If this line intercepts with the peak of the quadratic regression curve, which also
corresponds to a value close to 1 on the Y axis, the accurate perception of tension affordance can be determined. However, this is only seen
at recreational level.
The meaning of expertise in badminton 1193
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affordances of string tensions. Is that true? To
answer this question, we need to find out why expert
players prefer higher string tension even though they
were able to produce equally effective power strokes
with all string tensions?
To begin with, we must first consider the effect of
string tension on the dynamics of the shuttlecock
after impact. In our method for displaying visual
information about string tension, a reflective mar-
ker ball was dropped onto each set of strings from
the same height so observers could see the resulting
bounce height. This was similar to the method in
Warren et al. (1987) who investigated perception of
elasticity. The resulting bounce height increased
with decreasing string tension because the restitu-
tion coefficient (V
out
/V
in
)ishigherforlowerstring
tensions (as reported by Elliott, 1982). This tension
effect was directly evident in novice striking perfor-
mance, where we noticed that the lower the ten-
sion, the faster the shuttlecock after impact. The
implication is that variations in novice performance
were purely determined by the elasticity of string
tension.
In producing a power stroke, novice players
merely used elbow flexion and extension with little
follow through after striking. Skilled players per-
formed strokes quite differently than less skilled
players. Both recreational and expert players used a
full body motion starting with a side stance, then
swinging the racquet in a series of movements at
major joints starting with the ankle and knee, and
proceeding up to wrist and finger joints proximal to
the racquet. These motions were similar to those
exhibited in long distance over-arm throwing which
entail a well-timed sequence of movements along
these adjacent joints (Jöris, van Muyen, van Ingen
Schenau, & Kemper, 1985; Zhu, Dapena, &
Bingham, 2009). This timing is acquired through
the extensive practice that eventually yields expert
performance. Recreational players were able to
increase the impulse (or total force of impact) in
their power strokes by swinging the racquet faster.
This also shortened the duration of contact between
racquet and shuttlecock so that maximum energy
was transferred to the shuttlecock. This transfer
was facilitated, in turn, by a stiffer string bed.
Thus, higher string tension yielded better perfor-
mance for recreational players.
Expert players were also able to produce faster
racquet speeds as were the recreational players, but
obviously, they were doing something more to
enable them to maintain the resulting high shuttle-
cock speeds despite variations in string tensions.
Presumably, expert players were able to use wrist
and finger flexion to increase speed at the racquet
head even more to compensate for the loss of energy
when using lower string tensions. Although the time
allowed for the string bed to be stretched is minimal
in their fast swings, expert players must take advan-
tage of the longer dwell time provided by lower
string tension (Brody & Knudson, 2000) to swing
the racquet with additional acceleration. Skilled
human movements often demonstrate motor equiva-
lence, which refers to the capability of the motor
system in re-organising the available movement
parameters in order to achieve the same motor out-
comes (Hebb, 1949; Newell & Corcos, 1993). In our
case, the perception of lower string tensions by
expert players stimulated the expert motor system
to alter the striking motion by increasing the flexion
of wrist and fingers during impact, so that the addi-
tional speed can be generated to maintain high speed
of the shuttlecock after impact. However, this
method for generating additional speed comes with
a cost: it takes more energy and may cause fatigue.
For this reason, high string tensions are preferred by
the experts.
To investigate whether the expert players did
employ this strategy to yield the consistent shuttle-
cock speeds despite variations in string tensions, an
additional analysis was performed. If the racquet was
swung to make contact with the suspended shuttle-
cock at a constant angle, increasing the flexion of
wrist and fingers during impact would result in a
directional change of travel of the shuttlecock after
impact (travelling downward more). The expert
strokes were analysed with respect to two angles:
the angle of the racquet at the moment of contact
(“α”in Figure 3), and the angle of the shuttlecock
after impact (“β”in Figure 3), reflecting the direc-
tional change of travel.
This analysis was performed using only the
extremes of string tension variations: the lowest
(16 and 18 lbs) and the highest (28 and 30 lbs) string
Figure 3. Illustration of racquet angle (α) during impact and
shuttlecock angle (β) after impact.
1194 Q. Zhu
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tensions. As revealed by a one-way repeated mea-
sures ANOVA, the string tension did not affect,
α, the angle of the racquet at the moment of contact,
(F(1, 3) = 0.86, P> 0.05). The mean αwas 21.5
degrees (±7.7). However, a change in βto a greater
downward angle for lower string tensions was sig-
nificant, (F(1, 3) = 14.07, P< 0.05, η
2
= 0.82).
As shown in Figure 4A, lower string tension cor-
responded to a greater mean angle, suggesting that
expert players flexed their wrist and fingers more.
The same ANOVA performed on the speeds yielded
no tension effect, (F(1, 3) = 8.90, P> 0.05), as
shown in Figure 4B. This confirmed that the extra
flexion of wrist and fingers used to accommodate the
lower string tension was effective in generating
equally fast shuttlecock speeds as with higher string
tension. This analysis suggests that expert players
should be considered successful in perceiving the
affordance of string tension, because by selecting
the higher string tensions, they would not have to
increase flexion of wrist and fingers (at greater cost
in energy) to produce effective power strokes.
It is worth noting that selection of the optimal
string tension was equivalent across different percep-
tual modes. Although the mean preferred tensions
varied depending on motor expertise, no mean
change was found for different perceptual modes,
suggesting that similar tension can be perceived by
listening to the sound of impact, by watching the
bouncing event, or by pressing the string bed.
Warren et al. (1987) compared use of visual and
auditory perception of the elasticity of bouncing
balls, and found that human observers could accu-
rately judge the elasticity and then use that informa-
tion to control performance of a bounce pass with
the balls. Our results replicated this finding and
showed in addition that the elasticity could be per-
ceived haptically as well. The same tensions were
subsequently chosen after hitting where the three
modes could have been combined. The variability
of the judgments indicated, however, that haptic
perception of string tension was less reliable.
Players are more experienced in both hearing and
seeing the effects of string tension on power strokes
and our results may simply reflect this fact. The
findings are also consistent with the hypothesis of
specification in the global array. According to
Stoffregen and Bardy (2001), perceptual information
is specified solely in the global array, where the
higher-order relations exist across different forms of
energy. In this sense, the perceptual information
about the optimal string tension must exit in visual,
acoustic, haptic, or the mixed arrays, and can be
specified by the pattern of energy exhibited in each
perceptual event presented to the perceiver. The
perceivers must have picked up the same informa-
tion from different arrays to detect the same optimal
string tension. However, different frames of refer-
ence might be used depending on the experience of
the perceiver, which resulted in different optimal
tensions selected by players at different levels of
expertise.
Finally, it was clear in our results that the meaning
of string tension to badminton players depended on
their motor expertise. For novice players, lower
string tensions were better, but they failed to per-
ceive this well. Presumably, as novice players
develop motor expertise, the affordance of string
tension for a power stroke becomes more salient
and better perceived. It changes accordingly from
the lower tensions to the higher, which were selected
in common by recreational and expert players. The
affordance itself was a function of skill level as was
the ability to perceive the affordance. The nature of
the affordance continued to change with continued
development of skill from recreational to expert
players. The meaning of true expertise emerged as
an ability to perceive changes in the affordance of
string tension and to modify one’s action appropri-
ately, but at a cost. However, additional research will
be required to confirm this last conclusion.
In sum, we showed that badminton string tension
constrained striking performance of the power stroke
for novice and recreational players, but not for
expert players. Player’s perception of the optimal
A
B
25.00
75.00
60.00
45.00
30.00
Lower End Higher End
20.00
15.00
10.00
Mean Angle at MaxSpeed (degree)
Mean MaxSpeed (m.s–1)
Tension
(
Ib
)
Figure 4. The mean angle and mean maximum speed of the
shuttlecock after impact as a function of string tension for expert
strokes. Error bars represent standard error of the mean.
The meaning of expertise in badminton 1195
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string tension was equivalent across different percep-
tual modes. The perception of the affordance of
string tension for a power stroke was dynamic in
that the affordance property became salient to
players as motor expertise developed, but also chan-
ged itself. When motor expertise was enhanced to
allow for more possibilities for action, energy effi-
ciency became an important factor in determining
the affordance of string tension.
Acknowledgements
The authors thank USA Badminton (Colorado
Springs, CO) and Yonex USA (Torrance, CA) for
sponsoring racquets and strings that were used in the
experiments. Thanks also to Bill Becker in the electro-
nic shop of Arts & Science Research Support at the
University of Wyoming. This research project was also
partially supported by a University of Wyoming NIH
INBRE equipment grant, and a Division of
Kinesiology and Health equipment grant.
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