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Purpose: 1) to analyze the reliability and validity of a simple computation method to evaluate force (F), velocity (v) and power (P) output during a countermovement jump (CMJ) suitable for use in field conditions; and 2) to verify the validity of this computation method to compute the CMJ Force-velocity (F-v) profile (including unloaded and loaded jumps) in trained athletes. Methods: Sixteen high-level male sprinters and jumpers performed maximal CMJs under six different load conditions (from 0 to 87 kg). A force-plate sampling at 1000 Hz was used to record vertical ground reaction force and derive vertical displacement data during CMJ trials. For each condition, mean F, v, and P of the push-off phase were determined from both force plate data (reference method) and simple computation measures based on body mass, jump height (from flight time), and push-off distance, and used to establish linear F-v relationship for each individual. Results: Mean absolute bias values were 0.9% (±1.6), 4.7% (±6.2), 3.7% (±4.8), and 5% (±6.8) for F, v, P and slope of the F-v relationship (SFv), respectively. Both methods showed high correlations for F-v profile related variables (r = 0.985 - 0.991). Finally, all variables computed from the simple method showed high reliability with ICC > 0.980 and CV < 1.0%. Conclusions: These results suggest that the simple method presented here is valid and reliable for computing CMJ force, velocity, power, and force-velocity profiles in athletes and could be used in practice under field conditions when body mass, push-off distance, and jump height are known.
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Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Note. This article will be published in a forthcoming issue of the
International Journal of Sports Physiology and Performance. The
article appears here in its accepted, peer-reviewed form, as it was
provided by the submitting author. It has not been copyedited,
proofread, or formatted by the publisher.
Section: Original Investigation
Article Title: Validity of a Simple Method for Measuring Force-Velocity-Power Profile in
Countermovement Jump
Authors: Pedro Jiménez-Reyes
1
, Pierre Samozino
2
, Fernando Pareja-Blanco
3
, Filipe
Conceição
4
, Víctor Cuadrado-Peñafiel
5
, Juan José González-Badillo
3
, and Jean-Benoît
Morin
6
Affiliations:
1
Department of Physical Activity and Sports Science, Universidad Católica San
Antonio de Murcia, Murcia, Spain.
2
Laboratory of Exercise Physiology, University of Savoy,
Le Bourget-du-Lac, France.
3
Physical Performance & Sports Research Center, University
Pablo de Olavide, Seville, Spain.
4
LABIOMEP, Porto Biomechanics, Laboratory, University
of Porto, Porto, Portugal.
5
University Complutense of Madrid, Spain.
6
Laboratory of Human
Motricity, Education Sport and Health, University of Nice Sophia Antipolis, Saint-Etienne, France.
Journal: International Journal of Sports Physiology and Performance
Acceptance Date: March 10, 2016
©2016 Human Kinetics, Inc.
DOI: http://dx.doi.org/10.1123/ijspp.2015-0484
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
VALIDITY OF A SIMPLE METHOD FOR MEASURING FORCE-VELOCITY-
POWER PROFILE IN COUNTERMOVEMENT JUMP
Pedro Jiménez-Reyes
Pierre Samozino
Fernando Pareja-Blanco
Filipe Conceição
Víctor Cuadrado-Peñafiel
Juan José González-Badillo
Jean-Benoît Morin
Type of article: ORIGINAL INVESTIGATION
Contact author: Pedro Jiménez-Reyes
Facultad de Deporte, Universidad Católica San Antonio de Murcia,
Campus de los Jerónimos s/n, 30107 Guadalupe, Murcia, Spain.
E-mail: peterjr49@hotmail.com; pjimenez@ucam.edu
Preferred running-head: FORCE-VELOCITY-POWER PROFILE IN CMJ
Word count for abstract: 250
Word count for main text: 3500
Tables: 3
Figures: 3
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Abstract:
Purpose: 1) to analyze the reliability and validity of a simple computation method to
evaluate force (F), velocity (v) and power (P) output during a countermovement jump (CMJ)
suitable for use in field conditions; and 2) to verify the validity of this computation method to
compute the CMJ Force-velocity (Fv) profile (including unloaded and loaded jumps) in
trained athletes. Methods: Sixteen high-level male sprinters and jumpers performed maximal
CMJs under six different load conditions (from 0 to 87 kg). A force-plate sampling at 1000
Hz was used to record vertical ground reaction force and derive vertical displacement data
during CMJ trials. For each condition, mean F, v, and P of the push-off phase were
determined from both force plate data (reference method) and simple computation measures
based on body mass, jump height (from flight time), and push-off distance, and used to
establish linear F-v relationship for each individual. Results: Mean absolute bias values were
0.9% (±1.6), 4.7% (±6.2), 3.7% (±4.8), and 5% (±6.8) for F, v, P and slope of the F-v
relationship (S
Fv
), respectively. Both methods showed high correlations for F-v profile related
variables (r = 0.985 0.991). Finally, all variables computed from the simple method showed
high reliability with ICC > 0.980 and CV < 1.0%. Conclusions: These results suggest that
the simple method presented here is valid and reliable for computing CMJ force, velocity,
power, and force-velocity profiles in athletes and could be used in practice under field
conditions when body mass, push-off distance, and jump height are known.
Keywords: jumping, Force-velocity relationship, lower limb explosive performance,
resistance training
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
INTRODUCTION
Lower limb ballistic movements, aimed at accelerating the body mass as much as
possible over one repetition of bilateral leg extension, are thought to play a key role in
physical performance
1
. Vertical jumps represent the most-used example of this type of
movement.
2-3
The use of devices such as force platforms (FPs), linear and rotary position
transducers, jump mats, accelerometers, and smartphone applications is now common to
assess the neuromuscular capabilities of athletes and enable the measurement of many kinetic
and kinematic parameters. The FP is one of the most widely-used sports laboratory
measurement tools,
4-6
and is considered the gold standard for determining the mechanical
outputs of sport movements such as jumping. FPs are used to measure the ground reaction
force, derive the velocity of the center of mass (COM), and calculate the power generated
using the impulse-momentum relationships. Individual force-velocity (F-v) and power-
velocity relationships are usually determined to assess the athlete’s mechanical capabilities
profile.
7-8
These relationships describe the changes in external force generation and power
output with increasing movement velocity and may be summarized through three typical
variables: the theoretical maximal force at null velocity (F
0
); the maximal power output
(P
max
); and the theoretical maximal velocity at which the lower limbs can extend during one
extension under zero load (v
0
).
8
The ratio between F
0
and v
0
(i.e., the slope of the linear Fv
relationship) characterizes the F-v profile of the neuromuscular system.
8
It has been shown
that this F-v profile affects maximum impulse performances independently from the large
effect of P
max
, with the existence of an individually optimal F-v profile.
7-9
This optimal Fv
profile (S
Fv
opt), shown in squat jump (SJ) or countermovement jump (CMJ), corresponds to
the best balance between external force and maximal velocity capabilities.
7-9
Therefore, an
appropriate determination of the Fv relationship seems to be crucial to quantify the
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
mechanical capabilities of the lower limbs. However, these devices are expensive and thus
not available to many athletes and practitioners. In addition, data processing is usually
necessary following the collection of instantaneous force-time data, which can be time
consuming. To address these issues, a simple method for evaluating force, velocity and power
output during a SJ has been validated by Samozino et al.
10
However, the use of this method to
determine individual force- and power-velocity relationships in field conditions have not yet
been conducted during unloaded and loaded CMJs.
The aforementioned computation method has been validated for determining the Fv
profile in ballistic actions without countermovement.
8
However, the validity of the simple
computation method proposed for the SJ (Samozino et al 2008) for assessing the F-v profile
has not been confirmed for the CMJ. Therefore, our aims were: 1) to analyze the reliability
and validity of a simple computation method to evaluate force, velocity and power output
during a CMJ in field conditions; and 2) to verify the validity of this computation method to
evaluate the CMJ Fv profile (including unloaded and loaded jumps) in trained athletes.
METHODS
Subjects
Sixteen trained male Spanish national-/international-level sprinters and jumpers aged
23.1 ± 4.1 years, body mass 76.3 ± 6.4 kg and height 1.81 ± 0.06 m gave their written
informed consent to participate in this study, which was approved by the local ethical
committee of the University of Pablo de Olavide (Seville, Spain) and in agreement with the
Declaration of Helsinki. No physical limitations or musculoskeletal injuries that could affect
testing were reported. All athletes had a strength-training background ranging from 4 to more
than 6 years and were highly trained and familiar with the testing exercises.
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Experimental Design
The present study used a cross-sectional experimental design. All tests were
conducted at the same time of day, from 17:00 to 21:00. Each subject underwent
anthropometric assessment and performed unloaded and loaded CMJs on a FP to determine
the individual force-velocity and force-power output relationships. The mean vertical force
developed by the lower limbs during push-off (F), the corresponding mean vertical velocity
(v) and the mean power (P) and the Fv relationships were determined using both the FP and
the simple method for each trial.
Testing procedures
Jumping test. At the beginning of the testing session, the anthropometric
measurements (body mass, stature and height push-off, h
PO
) were performed. After a
standardized warm-up, consisting of 10 min of jogging on a treadmill, dynamic stretching
and preparatory vertical jumps, participants performed maximal CMJs under different
loading conditions (without loads and against five extra loads ranging from 17 to 87 kg in a
randomized order) to determine individual Fv relationships in CMJ. Before each jump,
participants were instructed to stand up straight and still on the center of the force plate with
their hands on their hips for unloaded conditions and on the bar (17 kg) for loaded jumps; this
hand position remained the same during the entire movement. From this position, participants
initiated a downward movement to reach a squatting position with a knee angle of about 90°
(although this angle was individual for each subject), followed immediately by a jump to
maximum height. Although subjects were expert in the exercise, verbal instructions were
given to control the degree of squatting achieved. The vertical distance covered by the COM
during push-off (h
PO
) was recorded from the FP for further analysis. At landing, subjects
were asked to touch down with the same leg position as when they took off, i.e. with
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
extended legs and maximal foot plantar flexion. If all these requirements were not met, the
trial was repeated. Two valid trials were performed with each load with 2 min recovery
between trials and 45 min between load conditions to minimize the likelihood of fatigue.
Equipment and data acquisition for the force plate method. The test was
performed in a Smith machine (Multipower Fitness Line, Peroga, Spain) that allowed a
smooth vertical displacement of the bar along a fixed vertical path. A standard force plate
(Bertec, Type 4060-15, Bertec Corporation, Columbus, OH, USA) was used to sample
vertical ground reaction force at 1000Hz. This device was interfaced with an analog to digital
converter MP100.2.0 (Biopac Systems Inc., Santa Barbara, CA, USA) connected to a PC.
Customized software (Isonet, Madrid, Spain) provided real-time collection and visualization
of F, v, and P output data from the best trial of each condition, determined from the averages
of instantaneous values recorded over the entire push-off phase. The vertical velocity of the
body center of mass was obtained from the integration over time of the vertical acceleration
signal obtained from FP measurements. The instantaneous vertical power was the product of
force and velocity at each instant. The push-off began when the velocity signal increased and
ended when the force signal at take-off fell to zero. In addition, h
PO
was determined from
integration of the velocity signal over time.
8
. For practical reasons, and because jump height
can be easily and very accurately obtained with a contact mat and even using an iPhone / iPad
app
11-12
that measures flight time, jump height was directly measured from flight time data
derived from the force signal.
Computation method. As has been previously reported,
10
it is possible to calculate
the values of F, v, and P during a jump from three simple variables; body mass (m), jump
height (h) and push-off distance (h
PO
). For a proper measurement of the h
PO,
the subject was
placed in a squat position, which was similar to the beginning of the concentric phase of a
CMJ and the heels on the floor. The vertical distance between the ground and the right leg
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
greater trochanter was measured at approximately 90° knee angle squat position, set using a
square (h
S
in Fig. 1) for each subject. h
PO
corresponded to the lower limbs length change
between the starting position and the moment of take-off. For convenience, it was assumed
that changes in the relative vertical positions of the greater trochanter and CM during a jump
could be neglected.
10
The value of h
PO
was then calculated as the difference between h
S
and
the extended lower limb length with maximal foot plantar flexion (greater trochanter to tiptoe
distance). h was determined from flight time (t
F
), applying the fundamental laws of
dynamics
13
with t
F
measured from the GRF-time signal.
=
1
8
𝑔𝑡
𝐹
2
(1)
Thus, as previously computed for SJ:
10
(2)
(3)
(4)
where m is the body mass in unloaded condition and body mass of the system (subject +
additional load) in loaded conditions, g is the gravitational acceleration, h is the jump height,
and h
PO
is the vertical push-off distance.
Fv relationships during countermovement jumps. As previously suggested,
8,14-16
Fv relationships were determined by least squares linear regressions. The best trial with each
load condition was used for analysis. Given that Pv relationships are derived from the
product of force and velocity, they were described by second-degree polynomial functions.
Fv curves were extrapolated to obtain F
0
(in N or N·kg
1
) and v
0
(in m·s
1
), which,
respectively, correspond to the intercepts of the Fv curve with the force and velocity axis.
( 1)
PO
h
F mg
h

2
gh
v
2
1
PO
ghh
P mg
h
()
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
The Fv profile was computed as the slope of the Fv linear relationship (S
Fv
, in
N·s·kg
1
·m
1
).
8
Values of P
max
(in W or W·kg
1
) were determined as P
max
= F
0
· v
0
/4.
8,17
Comparison of the two methods and statistical analysis
All data are presented as mean ± standard deviation (SD). Normality was checked
with the Shapiro-Wilk test before analyses. Test-retest absolute reliability was measured by
the standard error of measurement (SEM), which was expressed in relative terms through the
coefficient of variation (CV), whereas relative reliability was assessed by the intraclass
correlation coefficients and confidence interval (ICC, 95%CI) calculated using the one-way
random effects model. The SEM was calculated as the root mean square of total mean square
intra-subject variation. In the sport science field it has been suggested that CV values lower
than 10% are acceptable and ICC values greater than 0.90 are high, between 0.800.90
moderate, and lower than 0.80 questionable.
18
Concurrent validity was assessed using
different procedures. Linear regressions and Bland-Altman analyses
19
were performed on the
best trial of each load to compare the F, v, and P values obtained with the two methods. The
difference between the two methods (systematic bias) was computed for these parameters and
tested for each trial using a t-test for paired samples.
20
ICC values (relative validity),
between-methods differences in means (absolute validity in raw units and %) and CVs
(absolute validity in %) were calculated. The magnitude of correlation was assessed with the
following thresholds: <0.10, trivial; from 0.10 to 0.30, small; from 0.30 to 0.50, moderate;
from 0.50 to 0.70, large; from 0.70 to 0.90, very large; and from 0.90 to 1.00, almost
perfect.
21
For concurrent validity, values greater than 0.90 means that they are good
predictors.
18
For all statistical analyses, a P value of 0.05 was accepted as the level of
significance.
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
RESULTS
Reliability. Between-trials reliability was analyzed. ICC (95% CI) and CV values for
each of the kinetic and kinematic variables analyzed are reported in Table 1. A high
reliability was found for all variables (ICC > 0.980 and CV < 1.0%); in particular, h
PO
showed ICC of 0.998 (95% CI: 0.995 to 0.999) and CV of 0.4%.
Validity. Mean values ± SD of each kinetic and kinematic variable obtained from the
two methods are presented in Table 2. These data were obtained from the best trial against
each loading condition. The t-test for paired samples did not show significant differences
between the two methods for F, v, and P parameters. However, v
0
, P
max
and
S
Fv
values showed
significant (P < 0.05) differences between methods (Table 2). When the relationships
between both methods were individually adjusted almost perfect relationships were observed
for F (r = 0.985 0.999), v (r = 0.985 0.999), and P (r = 0.994 0.999). When considering
all subjects, F, v, P, F
0
, v
0
, P
max
and
S
Fv
variables obtained from the two trials were almost
perfectly correlated (r = 0.985 0.997, P < 0.001, Table 2). Slopes and y-intercept values of
the linear regressions were not significantly different from one and zero, respectively, except
for F
0
and S
Fv
(Table 2).
The Bland-Altman plots for F, v, and P are presented in Figure 2. The mean bias
between the two methods was 0.2 ± 18.1 N, 0.01 ± 0.02 m·s
-1
and 4.5 ± 22.5 W for F, v, and
P, respectively. The Bland-Altman plots for F
0
, v
0
, P
max
and S
Fv
are presented in Figure 3.
The mean bias between the two methods was -21.9 ± 79.3 N, 0.31 ± 1.00 m·s
-1
, 144.2 ± 441.9
W, and 20.7 ± 56.7 N·m·s
-1
for F
0
, v
0
, P
max
and S
Fv
, respectively. Expressed relative to the
mean values obtained with the FP method, these biases were 0.0 ± 1.0%, 0.0 ± 0.0% and 0.2
± 1.0%, respectively (Table 2), and 0.9 ± 1.6%, 4.7 ± 6.2%, 3.7 ± 4.8% and 5.0 ± 6.8% for
F
0
, v
0
, P
max
and S
Fv,
respectively (Table 2).
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
The ICC and CV values describing the concurrent validity of kinetic and kinematic
parameters computed from the simple method against the FP are reported in Table 3. The
relative (ICC) concurrent validity of the simple method was very good overall, with ICCs of
0.990 ± 0.009 (range 0.9770.998) and there was good absolute concurrent validity, with
CVs of 3.2 ± 2.8% (range 0.77.6%).
DISCUSSION
The main findings of this study were: 1) the simple method tested is valid for
evaluating force, velocity and power output during a CMJ based on only three simple
parameters (body mass, jump height and push-off distance); 2) this computation method is
also valid for assessing the Fv profile in CMJs in elite athletes, although these parameters
showed slightly higher bias (<6%) than those observed for force, velocity and power output
in each jump (<1%). In addition, F, V, P and h
PO
showed high reliability with ICC > 0.980
and CV < 1.0%. The simple computation method proposed here might offer an inexpensive
and easy alternative to assess CMJ performance and individualized F-v profile without the
need of expensive technology such as force plates or position transducers. However, h
S
cannot be measured and set along with the starting position immediately before the jump, as
occurs for SJ. The h
S
variable influences h
PO
, which plays a key role in the computations
performed from the simple method. However, h
PO
showed very high stability (reliability)
values in the trials using the FP (ICC: 0.998 (95% CI: 0.995 to 0.999) and CV: 0.4%). Thus,
in experienced athletes, h
PO
is reproducible between trials, so there should not be substantial
errors in F, V and P estimations when using the simple method. Therefore, the proposed
method allows accurate assessment of lower limb force, velocity and power values during
unloaded and loaded CMJs in field conditions, using only three simple parameters (body
mass, jump height and h
PO
).
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Objectively assessing performance in order to individualize training programs is one
of the main problems faced by strength and conditioning coaches. The search for a simple
field evaluation method has given rise to major concerns in the scientific literature for several
decades.
10,22-24
The equations used for this study have been previously applied in unloaded SJ
conditions.
10,24
These equations come from computations based on fundamental laws of
mechanics, and no postulates in conflict with reality were required. That said, the biases
introduced by the simplifications and approximations associated with this approach were
shown to be very low and trivial (average of 0.1%, ranging from 0.0% to 0.2%) for F, V and
P computed using both unloaded and loaded CMJs, which supports its validity. These results
extend experimental conclusions drawn for pure concentric SJs
8,10
to an exercise (CMJ) that
is more frequently used and suitable in sports training and testing.
25
The only basic postulates
admitted here were those inherent to all studies applying Newton’s laws to the whole human
body considered as a system represented by its center of mass.
7-10,24,26-27
Some of these
assumptions include: equality between average force over distance and average force over
time; and average power being equal to the product of average force and average velocity.
A measurement method is considered valid if it measures what it intends to measure.
This implies that this method is suitable and reliable. The suitability of the proposed method
is supported by the power values obtained, which are in accordance with a previous study
10
that considered SJ. The relationships observed between the values obtained by the proposed
method versus those measured by the FP for F, V and P were r = 0.995 0.997 (P < 0.001,
Table 2). The magnitude of these relationships were even higher than those observed by
Samozino et al.
10
for F, V and P in SJ (r = 0.96 0.98). Moreover, the mean bias and the
limits of agreement presented in Bland-Altman plots (Fig. 2) showed great accuracy for F, V
and P parameters during CMJ. The difference between data measured by FP and those
obtained from this computation method appears to be unaffected by the magnitude of the F, V
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
and P parameters, which is manifested by the negligible association shown in the Bland-
Altman plot (mean bias between the two methods was 0.2 ± 18.1 N, 0.01 ± 0.02 m·s
-1
and 4.5
± 22.5 W for F, v, and P, respectively, Fig. 2). The absolute bias is a key parameter in
synthesizing the validity and the accuracy of measurement method, since it considers both
systematic bias and random errors (standard deviation of the differences). This represents the
mean error in each measurement. In the present study, the absolute bias values were less than
1% for F, V and P. These absolute bias values are even lower than those reported previously
for these parameters (3%) when comparing the same computation method with FP
measurements during a concentric only jump.
10
This may be because the CMJ is a more
natural and more practiced exercise than SJ. Furthermore, very high concurrent validity was
shown for F, V and P (ICC > 0.997 and CV < 1.5%) and for theoretical maximal values of F,
V and P, and S
Fv
(ICC > 0.970 and CV < 8.0%). Thus, the present study demonstrates an
accurate and reproducible simple field method to evaluate force, velocity, and power output
of lower limb extensor muscles during a specific jump test (CMJ) with a precision similar to
that obtained with specific, more costly and less practical laboratory ergometers.
In addition to analyzing isolated SJs or CMJs, determining the F-v mechanical profile
of the lower limb neuromuscular system might help to maximize neuromuscular performance
in field conditions.
7-9
The present study supports the validity of this simple method for
computing the F-v profile during a CMJ test, which is a commonly used exercise in sports
training and testing and only had been validated during pure concentric jumps.
8
Although v
0
,
P
max
and S
Fv
values showed significant differences between methods, all these parameters
showed low absolute biases (ranging from 1% to 5%). These values are similar to those
previously reported for these variables measured during lower limb maximal extensions
without previous countermovement.
8
Both methods also showed high correlations for F
0
, v
0
,
P
max
and
S
Fv
variables (r = 0.985 0.991, Table 2). In addition, the Bland-Altman plots
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
showed low bias between the two methods (Fig. 3), although in all the analyses performed,
these theoretical variables (F
0
, v
0
, P
max
and S
Fv
) showed greater bias and lower validity values
than those computed for each jump (F, V, P). A plausible explanation for these results might
be because the theoretical variables are estimations extrapolated from the F, V, P, which are
estimated too. For this reason the errors might be accumulative decreasing the validity in
these parameters. Finally, all variables computed from the simple method showed high
reliability with ICC > 0.980 and CV < 1.0% (Table 1). These results support the validity and
reliability of the proposed theoretical approach and simple method to compute F-v profiles in
highly trained athletes during CMJ.
The main limitation of this method is the assumption that h
PO
is the same as the one
which was computed prior to the jump. However, h
PO
showed high reproducibility between
trials (ICC: 0.998 (95% CI: 0.995 to 0.999) and CV: 0.4%). Therefore, there should not be
substantial errors in F, V and P estimations due to h
PO
measurements when using the simple
method presented here. In this sense, it is important to note that h
PO
is reliable and constant
for a given subject and what is more important is that the computation of h
PO
is individual
and consistent between trials. Assuming there might be inter-individual differences in the
adjustment of CMJ depth when targeting 90 degrees knee angle, we use each individual’s
own h
PO
for the most comfortable CMJ depth with an angle close to 90°, and make sure that
each subject reaches his/her own CMJ depth during the jump trials for a correct F-v profile
computation.
PRACTICAL APPLICATIONS AND CONCLUSIONS
In conclusion, the accuracy and reliability of the proposed theoretical computations
were in line with those observed when using laboratory ergometers such as force plates.
Therefore, the proposed method, based on only three simple parameters (body mass, jump
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
height and h
PO
), allows accurate assessment of lower limb force, velocity and power
properties during unloaded and loaded CMJs in field conditions. This simple method allows
coaches and practitioners to identify individual P
max
and optimal F-v profiles to maximize
CMJ performance in field conditions. These findings extend those previously observed for
concentric only SJ
8,10
to CMJ, which is more frequently used in sports training and testing.
Due to the difficulty of accessing elite athletes to conduct laboratory measurements,
the ease of measuring biomechanical parameters in these subjects has scientific interest and
direct practical applications. A recent study has shown excellent reliability (ICC = 0.997, CV
= 3.4%) and excellent agreement with height measured using a FP (ICC = 0.997) for an
iPhone application (My Jump app ©).
11-12
Thus, the simple computation method and My
Jump app might be a low cost, easy-to-use application to assess CMJ performance (force,
velocity and power). These findings could help coaches to make evidence-based practice
decisions by monitoring the F-v profile of athletes’ lower limbs, which characterizes the ratio
between their maximal force and their maximal velocity capabilities. Coaches could use this
method to quantify individual athlete’s P
max
and F-v profiles, and individualize their training
regimes accordingly.
28
ACKNOWLEDGMENTS
The authors thank all the athletes who participated as subjects in this study. No sources of
funding were used in the preparation of this article.
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
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Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
17. Vandewalle H, Peres G, Heller J, Panel J, Monod H. Force-velocity relationship and maximal
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Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Figure 1 The three key positions during a vertical countermovement jump and the three
distances used in the proposed computations.
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Figure 2 Bland and Altman plot of differences between the force plate and computation
method for: (A) force, (B) velocity, and (C) power. Upper and lower horizontal dotted lines
represent the limits of agreement (mean ± 1.96 SD of the difference between methods).
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Figure 3 Bland and Altman plot of differences between the force plate and computation
method for: (A) the theoretical maximal force at null velocity (F
0
), (B) the theoretical
maximal velocity under zero load (v
0
), (C) the theoretical maximal power output (P
max
), and
(D) the slope of the linear Fv relationship (S
Fv
). Upper and lower horizontal dotted lines
represent the limits of agreement (mean ± 1.96 SD of the difference between methods).
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Table 1. Relative (intraclass correlation coefficients, ICC with 95% confidence intervals,
95% CI) and absolute (coefficient of variation, CV) reproducibility of kinetic and kinematic
variables analyzed during countermovement jump.
ICC (95% CI)
CV (%)
From force plate
h
PO
0.998 (0.995 to 0.999)
0.4
h
1.000 (0.999 to 1.000)
0.2
F
0.999 (0.998 to 1.000)
0.3
V
0.985 (0.959 to 0.995)
0.7
P
1.000 (0.999 to 1.000)
0.2
From Simple Method
F
1.000 (0.999 to 1.000)
0.2
V
1.000 (0.999 to 1.000)
0.1
P
1.000 (0.999 to 1.000)
0.3
Data are mean ± SD, n = 16
h
PO
: displacement of the center of mass from the beginning of concentric phase to the time of take-off
h: jump height calculated from aerial time measured from force plate
F: mean vertical force developed by the lower limbs during push-off
V: mean vertical velocity developed by the lower limbs during push-off
P: mean power output developed by the lower limbs during push-off
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Table 2. Mean ± Standard deviation, mean bias (%) and relationships between both methods
for mean force, velocity and power output, and force-velocity relationships.
Force
Plate
Method
Computation
Method
Mean Bias
(%)
Pearson
correlation
coefficient (r)
Slope of
the linear
regression
line
a
y Intercept
of the linear
regression
line
Computation Method
F (N)
1758 ± 131
1769 ± 129
0.0 ± 1.0
0.995*
0.98
35
v (m·s
-1
)
1.61 ± 0.07
1.61 ± 0.07
0.0 ± 0.0
0.996*
0.97
0.04
P
(W)
2839 ± 319
2847 ± 317
0.2 ± 1.0
0.997*
1.02
-47
F-v relationships
F
0
(N)
2547 ± 236
2541 ± 253
0.9 ± 1.6
0.989*
1.07
-196
b
v
0
(m·s
-1
)
5.27 ± 1.69
5.59 ± 2.13
4.7 ± 6.2
0.991*
1.25
-0.99
P
max
(W)
3320 ± 839
3464 ± 1017
3.7 ± 4.8
0.989*
1.20
-518
S
Fv
(N·s·m
-1
)
-528 ± 153
-507 ± 169
5.0 ± 6.8
0.985*
1.05
46
b
F: mean vertical force developed by the lower limbs during push-off
v: mean vertical velocity developed by the lower limbs during push-off
P: mean power output developed by the lower limbs during push-off
F
0
: the theoretical maximal force at null velocity,
v
0
: the theoretical maximal velocity at which lower limbs can extend during one extension under zero
load
P
max
:
Maximal power output against different loading conditions
S
Fv
: slope of the linear force-velocity relationship
* P < 0.001
† Significant differences between methods (P < 0.05)
a
Not significantly different from unity
b
Significantly different from 0
Validity of a Simple Method for Measuring Force-Velocity-Power Profile in Countermovement Jump
by Jiménez-Reyes P et al.
International Journal of Sports Physiology and Performance
© 2016 Human Kinetics, Inc.
Table 3. Relative (intraclass correlation coefficients, ICC with 95% confidence intervals,
95% CI) and absolute (coefficient of variation, CV) concurrent validity of kinetic and
kinematic variables computed from Simple Method.
ICC (95% CI)
CV (%)
Computation Method
F (N)
0.998 (0.997 to 0.998)
0.7
v (m·s
-1
)
0.998 (0.997 to 0.998)
1.4
P
(W)
0.998 (0.998 to 0.999)
0.9
F-v relationships
F
0
(N)
0.991 (0.976 to 0.997)
1.2
v
0
(m·s
-1
)
0.977 (0.935 to 0.992)
7.6
P
max
(W)
0.980 (0.944 to 0.993)
5.5
S
Fv
(N·s·m
-1
)
0.988 (0.966 to 0.996)
4.8
F: mean vertical force developed by the lower limbs during push-off
v: mean vertical velocity developed by the lower limbs during push-off
P: mean power output developed by the lower limbs during push-off
F
0
: the theoretical maximal force at null velocity,
v
0
: the theoretical maximal velocity at which lower limbs can extend during one extension under zero
load
P
max
:
Maximal power output against different loading conditions
S
Fv
: slope of the linear force-velocity relationship
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This study investigated the effects of a 3-week power-oriented resistance training programme performed at moderate altitude on the lower-limb maximal theoretical power and force-velocity (F-V) imbalance of elite judokas. Twenty-two elite male judokas were randomly assigned to either a hypobaric hypoxia or normoxia group. Mechanical outputs from an incremental loaded countermovement jump test were assessed at sea level, before and after training, and 1 week later. Results indicated an increase in the maximal theoretical force and a reduction in the F-V imbalance both at moderate altitude and sea level. Altitude training induced additional benefits when compared to sea level for F-V imbalance (8.4%; CI: 0.3, 17.3%), maximal theoretical power (2.09 W·kg⁻¹; CI: 0.13, 4.52 W·kg⁻¹) and force (1.32 N·kg⁻¹; CI: −0.12, 2.96 N·kg⁻¹), jump height (3.24 cm; CI: 2.02, 4.80 cm) and optimal maximal theoretical force (1.61 N·kg⁻¹; CI: 0.06, 3.60 N·kg⁻¹) and velocity (0.08 m·s⁻¹; CI: 0.00, 0.17 m·s⁻¹) after the training period. The hypoxia group achieved their best results immediately after the training period, while the normoxia group achieved them one week later. These results suggest that a power-oriented resistance training programme carried out at moderate altitude accelerates and improves the gains in lower-limb muscle power, while minimizing lower-limb imbalances. Therefore, it seems appropriate to compete immediately after the return to sea level and/or use altitude training as a tool to improve muscle power levels of athletes without tapering goals, especially in highly trained power athletes, since their window of adaptation for further power enhancement is smaller. Highlights • A 3-week power-oriented resistance training programme improved lower-limb mechanical outputs of elite judokas both at moderate altitude and sea level; training at moderate altitude increases and accelerates these improvements, reducing athletes’ imbalances. • It may be optimal for judokas to compete immediately after the return to sea level and/or use altitude training as a tool to improve muscle power levels of athletes without tapering goals, especially in highly trained power athletes, since their window of adaptation for further power enhancement is attenuated. • Athletes should ensure they possess adequate strength levels before employing a power-oriented training programme to potentiate further improvements in muscle power.
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Recent studies have brought new insights into the evaluation of power-force-velocity profiles in both ballistic push-offs (e.g. jumps) and sprint movements. These are major physical components of performance in many sports, and the methods we developed and validated are based on data that are now rather simple to obtain in field conditions (e.g. body mass, jump height, sprint times or velocity). The promising aspect of these approaches is that they allow for a more individualized and accurate evaluation, monitoring, and training practices; the success of which are highly dependent on the correct collection, generation and interpretation of athletes' mechanical outputs. We therefore wanted to provide a practical vade mecum to sports practitioners interested in implementing these power-force-velocity profiling approaches. After providing a summary of theoretical and practical definitions for the main variables, we have first detailed how vertical profiling can be used to manage ballistic push-off performance with emphasis on the concept of optimal force-velocity profile and the associated force-velocity imbalance. Further, we have discussed these same concepts with regards to horizontal profiling in the management of sprinting performance. These sections have been illustrated by typical examples from our own practice. Finally, we have provided a practical and operational synthesis, and outlined future challenges that will help in further developing these approaches.
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This study sought to lend experimental support to the theoretical influence of force-velocity (F-v) mechanical profile on jumping performance independently from the effect of maximal power output (P max ). 48 high-level athletes (soccer players, sprinters, rugby players) performed maximal squat jumps with additional loads from 0 to 100% of body mass. During each jump, mean force, velocity and power output were obtained using a simple computation method based on flight time, and then used to determine individual linear F-v relationships and P max values. Actual and optimal F-v profiles were computed for each subject to quantify mechanical F-v imbalance. A multiple regression analysis showed, with a high-adjustment quality (r²=0.931, P<0.001, SEE=0.015 m), significant contributions of P max , F-v imbalance and lower limb extension range (h PO ) to explain interindividual differences in jumping performance (P<0.001) with positive regression coefficients for P max and h PO and a negative one for F-v imbalance. This experimentally supports that ballistic performance depends, in addition to P max , on the F-v profile of lower limbs. This adds support to the actual existence of an individual optimal F-v profile that maximizes jumping performance, a F-v imbalance being associated to a lower performance. These results have potential strong applications in the field of strength and conditioning.
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My Jump Health and Fitness iOS 7.0 or later; Optimised for iPhone 5, iPhone 6 and iPhone 6 Plus. Compatible with iPhone, iPad and iPod touch. $A7.49 Current version is V.2.1 which has iPhone 6 and iPhone 6 Plus support, and iOS8 support. No trial version is available. Vertical jump is a widely used measure of functional performance in athletic and non-athletic populations.1 My Jump is a low-cost, easy-to-use application which integrates with the video camera to assess vertical jump performance (figure 1). The in-app settings allow slow-motion playback for easy identification of the video frame in which jump take-off and landing occurs. The app determines the number of …
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A simple test for the measurement of mechanical power during a vertical rebound jump series has been devised. The test consists of measuring the flight time with a digital timer (0.001 s) and counting the number of jumps performed during a certain period of time (e.g., 15–60 s). Formulae for calculation of mechanical power from the measured parameters were derived. The relationship between this mechanical power and a modification of the Wingate test (r=0.87, n=12 ) and 60 m dash (r=0.84, n=12 ) were very close. The mechanical power in a 60 s jumping test demonstrated higher values (20 WkgBW–1) than the power in a modified (60 s) Wingate test (7 WkgBW–1) and a Margaria test (14 WkgBW–1). The estimated powers demonstrated different values because both bicycle riding and the Margaria test reflect primarily chemo-mechanical conversion during muscle contraction, whereas in the jumping test elastic energy is also utilized. Therefore the new jumping test seems suitable to evaluate the power output of leg extensor muscles during natural motion. Because of its high reproducibility (r=0.95) and simplicity, the test is suitable for laboratory and field conditions.
To investigate the influence of skeletal muscle fiber composition on the mechanical performance of human skeletal muscle under dynamic conditions, 34 physical education students with differing muscle fiber composition (M. vastus lateralis) were used as subjects to perform maximal vertical jumps on the force-platform. Two kinds of jumps were performed: one from a static starting position (SJ), the other with a preliminary counter-movement (CMJ). The calculated mechanical parameters included height of rise of center of gravity (h), average force (F), net impulse (NI) and average mechanical power (W). It was observed that the percentage of fast twitch fibers was significantly related (p< 0.05-0.01) to these variables in SJ condition and also to h and NI of the positive work phase in CMJ. It is concluded that skeletal muscle fiber composition also determines performance in a multijoint movement. The result is explainable through the differences in the mechanical characteristics of the motor units and their respective muscle fibers.