Advances in Physical Education
2013. Vol.3, No.1, 10-14
Published Online February 2013 in SciRes (http://www.scirp.org/journal/ape) http://dx.doi.org/10.4236/ape.2013.31002
10
An Effect of the Elastic Energy Stored in the Muscle-Tendon
Complex at Two Different Coupling-Time Conditions during
Vertical Jump
Sukwon Kim
Department of Physical Education, Research Institut e of Physical Education, Chonbuk National University,
Jeonju, South Korea
Received October 9th, 2012; revised November 12th, 2012; accepted November 24th, 2012
A study was performed to evaluate effects of elastic energy stored pre-stretch on the mechanical work
output while performing vertical jump. Eight male volunteers of age between 21 - 29 years old partici-
pated in the present study. The present study hypothesized that the vertical jump height during counter-
movement jumps (CMJ) would be higher than that during squat jump (SJ). During squat jump, a volun-
teer paused 0.5 sec before making upward movement. The results showed that ground reaction forces and
vertical jump displacements were higher in CMJ in comparison to SJ. The study concluded that part of the
positive work measured did derive from the recoil of the elastic component of the muscle-tendon com-
plex.
Keywords: Coupling-Time; Vertical Jump; Elastic Energy
Introduction
During jumping, walking, or running, which causes the verti-
cal displacement of the mass center of the body, the legs con-
tinue to flex and extend the joints in the lower extremities, such
as hips, knees, and ankles (Young, 2003; Cavagna et al., 1971;
Bobbert & Schenau, 1988; Zajac et al., 2002). The mechanical
analysis of patterns of walking, running, and jumping has been
researched at a level of the lower extremities (Voigt et al., 1995;
Bobbert et al., 1986; Umberger, 1998). However, the effects of
the elastic energy stored and used in the muscle-tendon complex
during vertical jumping have not been thoroughly explained
(Young, 2003; Cavagna et al., 1971; Bobbert & Schenau, 1988;
Zajac et al., 2002; Voigt et al., 1995; Bobbert et al., 1986).
Without the combination of flexion and extension of the
joints, humans could not walk, run, or jump properly (Voigt et
al., 1995; Bobbert et al., 1986). During jumping, walking, and
running, flexion of the legs results in stretching of the muscles,
like the vastus lateralis, gluteus maximums, and gastrocnemius
and tendons, like Achilles tendon. Many scientists (Komi, 2000;
Morgan et al., 2000; Edman & Tsuchiya, 1996; Ettema et al.,
1990; Lee & Herzog, 2002; Bosco et al., 1987; Morgan et al.,
2000; De Ruiter et al., 2000) have thought that stretching of the
muscle-tendon complex would cause the recoil of elastic energy ,
which produces a certain amount of mechanical work without
utilization of chemical energy. This stored elastic energy is
reused for the next following concentric contraction. However,
the correlation between pre-stretch of the muscle-tendon com-
plex in the lower extremity and vertical jump height has been a
very sophisticated and disputed fact since the 19th century.
The goal of the present study was to evaluate effects of
stored elastic energy in muscle-tendon complex in the lower
extremity on mechanical work output represented by the height
of the vertical jump. The experimental data is collected at two
different coupling time conditions: 1) countermovement jump
(CMJ); and 2) Squat jump (SJ).
The present study hypothesized that the vertical jump height
during countermovement jumps would be higher than the ver-
tical jump height during squat jump.
Methods
Subject
Eight participants were recruited from the general university
population to participate in this study. All participants were
ranged in age between 21 - 29 years old. They were normally
involved in at least one physical activity that requires jumping
or hopping. In order for subjects to be familiar with jumping
elements, the participants were recruited depending on famili-
arity with jumping.
Each participant completed an informed consent form ap-
proved by the University’s Internal Review Board (IRB). They
had no history of lower extremity injury, surgery, or discomfort
in the lower extremities. If they were injury free, they were
qualified to continue the test. Otherwise, the participants were
removed from the experiment. Social characteristics, such as
ethnic background, were not considered.
Instrumentation
Kinematic and kinetic data were collected during each jump
trial. Kinematic data were collected in 2 dimensions using a
Motion Analysis Corporation video system. One NEC camera
was set at a height of 80 cm and a distance of 7 meters from the
force platform (Figure 1). The subject was filmed in the sagit-
tal plane as they performed the countermovement and squat
jumps. It recorded a field of view 304.5 cm × 228.5 cm (Figure
2). The camera was leveled using a bubble level. In order to

S. KIM
Figure 1.
Motion analysis equipment set-up.
Figure 2.
Fixation of Ho for CMJ and SJ by the photo-cell (Figure 4) and a field
of view.
optimize the image of the 5 reflective markers and the subjects,
the flood light was set behind the camera; one flood light was
used to enhance the brightness of the testing area to optimize
digitization process. The reflective markers were placed over the
skin at the position of five bony prominences (Figure 3); the
head of the fifth metatarsophalangeal, the lateral malleolus, the
lateral epicondyle, the greater trochanter, and the glenohumeral
joint. The four segments (Figure 3) were classified; Upper body
(between the glenohumeral joint and the greater trochanter),
Thigh (between the greater trochanter and the latera l epicondy le),
Shank (between lateral epicondyle and the lateral malleolus) and
Foot (between the head of the fifth metatarsophslangeal and the
lateral malleolus).
The reflector was set to stand 0.66 meter away from the west
edge of the force platform and the projector was set to stand 4.15
meters away from the east edge of the force platform (Figure 1).
It made a beep sound when the light to the reflector was dis-
turbed by an object; in this case, hip was the only one that dis-
turbed the light (Figure 4); the subjects controlled the squatting
height for the CMJ and SJ by themselves by jumping after a
beep sound. The use of the photo-cell was designed by the in-
vestigator to control and equalize the squat height during the
countermovement jump and the squat jump (Figures 2 and 4).
Kinetic data was collected on an AMTI force platform
(AMTI Inc. Model OR6-5-1). Force data in the vertical (Fz)
direction were collected at 1200 Hz using the Ariel Perform-
ance Analysis system (APAS). An AMTI signal amplifier
(Model SGA6-3) was used to amplify the analog signal before
it reached the APAS. Kinetic data were collected for 3 seconds,
Figure 3.
Placement of the reflective markers and classification of four segments.
Figure 4.
Control of the squat height by the photo-cell.
recording 90 frames for each jump. The ground contact period
at the lift-off during a pause and the peak ground reaction
forces during landing were monitored for general consistency
throughout the whole experiment. A trial was considered unac-
ceptable if the subject did not contact the ground with both feet
simultaneously, making two impact peaks, or if the ground
contact period at the lift-off is less than 0.5 second as lift-off
during squat jump.
Kinematic data were recorded for the same period by the
Motion analysis Corporation video system and transferred to
HU-M-AN software for digitizing. The digitization process was
processed manually by clicking the mouse over the reflective
markers on the computer screen. The distortion rate and the
distance rate were measured using 1 m × 1 m square and 1.905
meters stick bar. HU-M-AN was used to calculate kinematic
variables.
Experimental Protocol
The participants were asked to wear the shoes that he/she
wore during his/her physical activities. For the clear view of the
reflective markers, the participants were asked to wear short

S. KIM
pants and shirts without arm sleeves. Before the actual experi-
ments started, several practices were given to each subject on
the force platform in order for them to be familiar with the test
process. For example, the squat height had to be very same
during CMJs and SJs for each participant to equalize the poten-
tial energy during each jump. For this equalization, the investi-
gator used one set of the photo-cell (Figure 4) to match the
squat height in CMJs and SJs. Therefore, all participants had to
jump after hearing a beep sound from the photo-cell (Figures 2
and 4). The photo-cell was also used to fix the relative knee
angle. The investigator inspected the ground reaction force data
collected by the APAS system during the practice trials to de-
termine jump consistency. Feedback was given to the subjects
to help them improve their jump quality and consistency. All
subjects were given as many practice jumps as they wanted.
For the actual experiment, subjects were asked to stand on
the force platform in the sagittal plane from the camera. For all
jumps, the subjects were instructed to have arms cross over the
chest to minimize the effect of arm swing. For all jumps, each
subject began from a relaxed standing position and was in-
structed to jump as high as possible. For the countermovement
jumps (CMJs), subjects were instructed to extend (jump) verti-
cally hip, knee, and ankle joints after flexing them without a
delay between flexion and extension of each joint. For the
squatting jumps (SJs), each subject began from the standing
position, and was instructed to squat and wait for 0.5 second
before jumping. Each subject performed the five counter-move-
ment jump (CMJs) and five squat jumps (SJs) alternately with
about 50 - 60 second break between each jump.
Ground reaction force data collected for each subject were
divided by their body weight in order to express all kinetic data
in terms of body weight. When the 10 jumps had been com-
pleted, the investigator asked the participants about the fatigue
level in the lower extremities to assess the consistency of all the
jumps. If a subject’ ability to do 10 jumps in a row with the
break was not consistent, the investigator had given longer
break between each jump.
Data Analysis
Descriptive and inferential statistical analyses were per-
formed by utilizing the SPSS (IBM Corporation, USA). The
differences were evaluated using paired t-tests. The results were
considered as statistically significant when p  0.05.
Results
The goal of the present study was to compare the influence
of stored elastic energy in muscle-tendon complex in the lower
extremity on mechanical work out put represented by the height
of the vertical jump between Counter Movement Jump (CMJ)
and Squat Jump (SJ). The comparison in the peak ground reac-
tion force and the vertical displacement of vertical jump be-
tween CMJ and SJ was made. Relative knee angle was meas-
ured to see if there was a movement of segments during the
pause phase.
Relative Knee An gl e
The relative knee angle was measure in order to observe if
the pause between flexion and extension during SJ was cor-
rectly controlled. Figure 5 illustrates the relative knee angle
typical for SJ. There was no significant change in relative knee
Figure 5.
Example of relative knee angle curve during squat j ump.
angle during the pause phase in SJ for more than 0.5 seconds
(15 frames), which indicates that the pause was controlled suc-
cessfully during SJ. The mean relative knee angle in Figure 5
between the two vertical lines (a pause) was 78.41 ± 1.18.
Peak Ground Reaction Force
The peak ground reaction force was measured in each subject
in order to compare the ground reaction force exerted during
push-off between during CMJ and during SJ. Table 1 reports
the mean peak GRF during CMJ and SJ. In all subjects except
subject 1, mean of Peak GRF in CMJ was significantly higher
than mean of Peak GRF in SJ. For example, in Subject 6, the
Mean Peak GRF in the SJ was 1835 ± 56.85 and in the CMJ, it
was 2031.25 ± 57.09. In addition, paired t-test of individual
mean peak ground reaction force of CMJ and SJ (t = 4.449, df =
6, P = 0.0022) suggested that mean peak ground reaction forces
of CMJ was significantly higher than that of SJ.
Initial Height (Ho)
The most important different in the methodology of this
study from the other studies was that the investigator tried to
control the stored elastic potential energy by equalizing the
initial height at the push-off during both countermovement and
squat jumps. The set-up for Ho was the most important process
in the study since the photo-cell was to control Ho which rep-
resented the stored elastic potential energy. Table 2 illustrates
Ho in both CMJ an SJ. Paired t-test showed that the values of
Ho in CMJ and SJ were statistically insignificant (t = 0.535, df
= 7, P = 0.61). This result suggested that the values of Ho were
very close to each other suggesting that the stored elastic poten-
tial energy at Ho was said to be the same.
Vertical Jump Displacement
The vertical jump height in each jump was measure to ob-
serve the influence of stored elastic energy in muscle-tendon
complex in the lower extremity on mechanical work output re-
presented by the height of the vertical jump. All five jumps in
each condition which was Squat jump and Countermovement
jump was averaged out.
Figure 6 illustrates the comparison of vertical displacement
between Squat Jump and Countermovement Jump. Paired t-test
showed significantly higher displacement in CMJ in compare-
son to SJ (t = 4.26, df = 7, P = 0.004). The most increase was
performed in Subject 3. However, the Subject 1 jumped just
0.3% higher during CMJ. Table 3 demonstrates the percentage
increase in the vertical displacement of CMJ in comparison to
the vertical displacement of SJ.
12

S. KIM
Table 1.
Mean peak ground reaction force (N) in CMJ and SJ.
CMJ SJ
T-test
(P-value)
Subject 1 1835.25 ± 12.47 1866 ± 24.40 0.32
Subject 2 1350 ± 31.50 1480 ± 35.50 0.0003
Subject 3 1265 ± 6.20 1460 ± 49.22 0.0001
Subject 4 1727.5 ± 55.22 1827 ± 54.5 0.02
Subject 5 1835 ± 29.55 1905 ± 53.07 0.05
Subject 6 1834.25 ± 56.85 2031.25 ± 57.09 0.0006
Subject 7 1303.5 ± 25.3 1497.75 ± 2 1.09 0.0001
Subject 8 1420 ± 35.30 1460.75 ± 5.20 0.037
Table 2.
Average Ho (initial height (cm)) of CMJ and SJ.
Subject 1 2 3 4 5 6 7 8 MeanSD
CMJ 46.84 57.30 55.58 50.38 47.20 56.92 53.50 56.20 52.994.30
SJ 49.00 55.95 53.60 54.78 55.95 53.30 53.27 54.29 53.762.20
Figure 6.
Comparison of vertical displacement between squat jump and counter-
movement jump.
Table 3.
Percentage increase in CMJ in comparison to SJ in vertical displace-
ment.
Subject 1 2 3 4 5 6 7 8
0.3% 4.7% 7.0% 1.8% 5.0% 2.4% 1.6%3.5%
Discussion
The goal of the present study was to evaluate the influence of
stored elastic energy in muscle-tendon complex in the lower
extremity on mechanical work output represented by the height
of the vertical jump.
Stretching of and Potential Energy Created in Actin
and Myosin Filaments
In life, muscle fibers can be stretched up to 10% of their
length (Biewener et al., 1981). These large stretches are used to
gain optimal mechanical energy in muscles and elastic fibers.
The enhancement of performance during concentric contraction
followed by eccentric contraction can be explained by these
stretching (Voigt et al., 1995; Komi, 2000; Lee & Herzog, 2 002;
Morgan et al., 2000; Bullimore et al., 2008; Hodson-Tole &
Wakeling, 2010). In the present study, the initial height and
relative knee angle of each individual right before the take-off
for vertical jump was set to a fixed height for both trials (CMJ
and SJ) by utilizing the photo cell. If not controlled, greater
force could be produced in one case resulting in higher jump
displacement (Voigt et al., 1995). Active muscle resists stretch-
ing with a force greater than the isometric force (Lee & Herzog,
2002; Bosco et al., 1987; Bullimore et al., 2008; Cavagna et al.,
1985; Herzog & Leonard, 1997; Meijer et al., 1997). The force
attained after large, fast stretches was due to 1) a greater force
developed by each bridge (Hodson-Tole & Wakeling, 2010); or
2) an increased number of cross-bridge attachments (Lee &
Herzog, 2002; Proske & Morgan, 1999). The decrease in the
number of attached cross-bridges reduced the load-sustaining
ability of the fibers to result in the initial rapid lengthening.
However, the detached cross-bridges start to re-attach to the
thin filaments. The increase in the number of attached cross-
bridges restored the load-sustaining ability to cause the subse-
quent shortening when F (instaneous force) is not much larger
than Fo (maximal force at zero velocity).
Power and Performance Enhancement by Stored
Elastic Energy in the Muscle-Tendon Complex and
the Coupling Time
In agreement with the previous studies (Ettema et al., 1990;
Lee & Herzog, 2002; Bullimore et al., 2008; Cavagna et al.,
1985) peak ground reaction forces (i.e. concentric contraction)
before take-off and vertical displacement in the present study
were higher in CMJ than in SJ. This result may confirm that,
during eccentric contraction, elastic energy due to stretching
could be stored in the muscle-tendon complex for later use such
as concentric contraction, but, a coupling time could be a limit-
ing factor because stored elastic energy would dissipate rapidly.
The force-velocity relationship suggests that the force gener-
ated by a muscle is a function of its velocity (Lieber, 2002). For
example, force drops precipitously as muscle is allowed to
shorten. Nevertheless, the eccentric phase during flexion of the
lower limbs is considered to enhance performance in the con-
centric phase. Cavagna et al. (1971) found that elastic energy
stored in muscle-tendon complex would produce power en-
hancement during sprint running even after the force was sup-
posed to drop. Studies (Komi, 2000; Komi & Nicol, 2000)
found that the concentric phase without the eccentric phase
generated less ground reaction force than the concentric phase
following by the eccentric phase. However, studies found that
the period (i.e. coupling time) between the two contractions
was a key concern. Bosco and Rusko (2008) presented a study
of the coupling time during treadmill running at different
speeds using special soft shoes in addition to normal shoes. The
study measured the oxygen consumption to demonstrate the
energy consumed with soft shoes and normal shoes. The as-
sumption was that during running, because cushioning de-
creased the force between colliding bodies by increasing the
time collision, soft shoes would increase the coupling time,
costing more energy. As assumed, the results showed that run-
ning with soft shoes required greater energy consumption than
running with normal shoes. Their results suggested the effect of
coupling time as a limiting factor for recoil of elastic energy
which means that longer the coupling time, less possibility to
re-use the elastic energy stored in the muscle-tendon complex.
Also, the present study suggested that skel etal muscles could

S. KIM
14
be more efficient when using stored elastic energy in muscle-
tendon complex. In agreement with previous findings (Voigt et
al., 1995; Bosco & Rusco, 2008), the CMJ showed better per-
formance results than SJ. During SJ conditions, concentric con-
traction took place 0.5 sec after the stretching. This suggested
that 0.5 sec was enough to dissipate the elastic energy in mus-
cle-tendon complex during vertical jump. Greater positive me-
chanical work due to greater ground reaction force during push-
off and vertical displacement suggested that the energy stored
was used to produce mechanical work during concentric con-
traction.
The conclusion was that part of the positive work measured
did not derive from transformation of chemical energy but it
was derived, without cost of chemical energy, from the recoil of
the elastic component of the muscle-tendon complex.
Assumptions
1) Muscle can absorb, store, and reutilize the potential en-
ergy.
2) During the negative work phase of the vertical jump, ex-
tensor muscles are stretched and elastic energy, produced while
stretching of the muscles, is stored in the muscle-tendon com-
plex and reutilized during the positive work phase.
3) Potential energy stored after stretching is used to enhance
the performance during shortening from a state of isometric
contraction.
4) 0.5 seconds delay during SJ is a long enough time for the
stored elastic energy to dissipate in heat.
5) Power produced in the lower extremity during the positive
work phase is proportionally related to vertical velocity.
6) An increased power (force × velocity) increases jump
height.
Acknowledgements
This paper was supported by research funds of Chonbuk Na-
tional University in 2012.
REFERENCES
Biewener, A., Alexander, R., & Heglund, R. (1981). Elastic energy sto-
rage in the hopping of kangaroo rats. Journal of Zoology, 195, 369-
383. doi:10.1111/j.1469-7998.1981.tb03471.x
Bobbert, M., Huijing, P., & Ingen Schenau, G. (1986). An estimation of
power output and work done by the human triceps surae muscle-
tendon complex in jumping. Journal of Biomec h an i c s , 19, 899-906.
doi:10.1016/0021-9290(86)90185-5
Bobbert, M., & van Ingen Schenau, G. J. (1988). Coordination in Verti-
cal Jumping. Journal of Biomechanic s , 21, 249-262.
doi:10.1016/0021-9290(88)90175-3
Bosco, C., & Rusko, H. (2008). The effect of prolonged skeletal muscle
stretch-shortening cycle on recoil of elastic energy and on energy
expenditure. Acta Physiologica, 119, 219-224.
Bosco, C., et al. (1987). The effect of pre-stretch on mechanical effi-
ciency of human skeletal muscle. Acta Physiol Scand, 131, 323-329.
doi:10.1111/j.1748-1716.1987.tb08246.x
Bullimore, S., MacItosh, B., & Herzog, W. (2008). Is a parallel elastic
element responsible for the enhancement of stead-state muscle force
following active stretch? The Journal of Experimental Biology, 211,
3001-3008. doi:10.1242/jeb.021204
Cavagna, G., Komarek, L., & Mazzoleni, S. (1971). The mechanism of
sprint running. Journal of Physiology, 281, 139-155.
Cavagna, G., Mazzanti, M., Heglund, N., & Citterio, G. (1985). Storage
and release of mechanical energy by active muscle: A non-elastic
mechanism? Journal of Experimental Biology, 115, 79-87.
De Ruiter, C., Didden, W., Jones, D., & De Haan, A. (2000). The
force-velocity relationship of human adductor pollicis muscle during
stretch and the effects of fatigue. Journal of Physiology, 526, 671-
681. doi:10.1111/j.1469-7793.2000.00671.x
Edman, K., & Tsuchiya, T. (1996). Strain of passive elements during
force enhancement by stretch in frog muscle fibres. Journal of Physi-
ology, 490, 191-205.
Ettema, G., Van Soest, A., & Juijing, P. (1990). The role of series elas-
tic structures in prestretch-induced work enhancement during isoto-
nic and isokinetic contractions. Journal of Experimental Biology, 154,
121-136.
Herzog, W., & Leonard, T. (1997). Depression of cat soleus forces fol-
lowing isokinetic shor t e n i ng . Journal o f Biomechanics, 30, 865-872.
doi:10.1016/S0021-9290(97)00046-8
Hodson-Tole, E., & Wakeling, J. (2010). The influence of strain and
activation on the locomotor function of rat ankle extensor muscles.
The Journal of Experimenta l Biology, 213, 318-330.
doi:10.1242/jeb.031872
Komi, P., & Nicol, C. (2000). Stretch-shortening cycle fatigue. In B.
McIntosh, & B. Nigg (Eds.), Biomechanics and biology of movement.
Champaign, IL: Human Kinetics Publishers.
Komi, P. (2000). Stretch-shortening cycle: A powerful model to study
normal and fatigued muscle. Journal of Biomechanics, 33, 1197-
1206.
Lee, H., & Herzog, W. (2002). Force enhancement following muscle
stretch of electrically stimulated and voluntarily activated human
adductor pollicis. The Journal of Physiology, 545, 321-330.
doi:10.1113/jphysiol.2002.018010
Lieber, L. R. (2002). Skeletal muscle structure and function, & plastici-
ty. Baltimore, MD: Lippincott Williams & Wilkins.
Meijer, J., Grootenboer, B., & Koopman, P. (1997). Fully isometric
length-force curves of rat muscle differ from those during and after
concentric contractions. Journal of Applied Biomechanics, 13, 164-
181.
Morgan, D., Whitehead, N., Wise, A., Gregory, J., & Proske, U. (2000).
Tension changes in the cat soleus muscle following slow stretch or
shortening of the contracting muscle. Journal of Physiology, 522,
503-513. doi:10.1111/j.1469-7793.2000.t01-2-00503.x
Proske, U., & Morgan, D. (1999). Do cross-bridge contribute to the ten-
sion during stretch of passive muscle? Journal of Muscle Research
and Cell Mobility, 20, 433-442. doi:10.1023/A:1005573625675
Umberger, B. (1998). Mechanics of the vertical jump and two-joint mu-
scles: Implications for training. Strength and Conditioning, 20, 70-74.
doi:10.1519/1073-6840(1998)020<0070:MOTVJA>2.3.CO;2
Voigt, M., Simnsen, E., Dyhre-poulsen, P., & Klausen, K. (1995). Me-
chanical and muscular factors influencing the performance in maxi-
mal vertical jumping after different pre-stretch load. Journal of Bio-
mechanics, 28, 293-307. doi:10.1016/0021-9290(94)00062-9
Young, W., & Behmm, D. (2003). Effects of running, static stretching
and practice jumps on explosive force production and jumping per-
formance. The Journal of Sports Medicine and Physical Fitness, 43,
21-27.
Zajac, F., Neptune, R., & Kautz, S. (2002). Biomechanics and muscle
coordination of human walking: Part I: Introduction to concepts, po-
wer transfer, dynamics and simulations. Gait and Posture, 16, 215-
232. doi:10.1016/S0966-6362(02)00068-1