Content uploaded by Pedro Jimenez-Reyes

Author content

All content in this area was uploaded by Pedro Jimenez-Reyes on Apr 04, 2016

Content may be subject to copyright.

“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 (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 (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 F–v

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 F–v

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 F–v 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 F–v

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 F–v 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 F–v 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 F–v 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 4–5 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.

ℎ =

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.

F–v relationships during countermovement jumps. As previously suggested,

8,14-16

F–v relationships were determined by least squares linear regressions. The best trial with each

load condition was used for analysis. Given that P–v relationships are derived from the

product of force and velocity, they were described by second-degree polynomial functions.

F–v 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 F–v 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 F–v profile was computed as the slope of the F–v 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 0.80–0.90

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 0.977–0.998) and there was good absolute concurrent validity, with

CVs of 3.2 ± 2.8% (range 0.7–7.6%).

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 F–v 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.

References

1. Cormie P, McCaulley GO, Triplett NT, McBride JM. Optimal loading for maximal power

output during lower-body resistance exercises. Med Sci Sports Exerc. 2007;39:340-349.

2. Bobbert MF, Gerritsen KG, Litjens MC, van Soest AJ. Why is countermovement jump height

greater than squat jump height? Med Sci Sports Exerc. 1996;28:1402-1412.

3. Klavora P. Vertical-jump tests: A critical review. Strength Cond. 2000;22:70-75.

4. Cormie P, Deane R, McBride JM. Methodological concerns for determining power output in

the jump squat. J Strength Cond Res. 2007;21:424-430.

5. Cormie P, McBride JM, McCaulley GO. Power-time, force-time, and velocity-time curve

analysis during the jump squat: impact of load. J Appl Biomech. 2008;24:112-120.

6. Gonzalez-Badillo JJ, Marques MC. Relationship between kinematic factors and

countermovement jump height in trained track and field athletes. J Strength Cond Res.

2010;24:3443-3447.

7. Samozino P, Edouard P, Sangnier S, Brughelli M, Gimenez P, Morin JB. Force-velocity profile:

imbalance determination and effect on lower limb ballistic performance. Int J Sports Med.

2014;35:505-510.

8. Samozino P, Rejc E, Di Prampero PE, Belli A, Morin JB. Optimal force-velocity profile in

ballistic movements--altius: citius or fortius? Med Sci Sports Exerc. 2012;44:313-322.

9. Jimenez-Reyes P, Samozino P, Cuadrado-Penafiel V, Conceicao F, Gonzalez-Badillo JJ, Morin

JB. Effect of countermovement on power-force-velocity profile. Eur J Appl Physiol.

2014;114:2281-2288.

10. Samozino P, Morin JB, Hintzy F, Belli A. A simple method for measuring force, velocity and

power output during squat jump. J Biomech. 2008;41:2940-2945.

11. Balsalobre-Fernandez C, Glaister M, Lockey RA. The validity and reliability of an iPhone app

for measuring vertical jump performance. J Sports Sci. 2015:1-6.

12. Stanton R, Kean CO, Scanlan AT. My Jump for vertical jump assessment. Br J Sports Med.

2015

13. Asmussen E, Bonde-Petersen F. Storage of elastic energy in skeletal muscles in man. Acta

Physiol Scand. 1974;91:385-392.

14. Bosco C, Belli A, Astrua M, et al. A dynamometer for evaluation of dynamic muscle work. Eur

J Appl Physiol Occup Physiol. 1995;70:379-386.

15. Rahmani A, Viale F, Dalleau G, Lacour JR. Force/velocity and power/velocity relationships in

squat exercise. Eur J Appl Physiol. 2001;84:227-232.

16. Yamauchi J, Ishii N. Relations between force-velocity characteristics of the knee-hip

extension movement and vertical jump performance. J Strength Cond Res. 2007;21:703-709.

“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

power on a cycle ergometer. Correlation with the height of a vertical jump. Eur J Appl Physiol

Occup Physiol. 1987;56:650-656.

18. Vincent WJ. Statistics in kinesiology. Champaign (IL): Human Kinetics. 1999;2nd ed.

19. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of

clinical measurement. Lancet. 1986;1:307-310.

20. Atkinson G, Nevill AM. Statistical methods for assessing measurement error (reliability) in

variables relevant to sports medicine. Sports Med. 1998;26:217-238.

21. Hopkins WG, Marshall SW, Batterham AM, Hanin J. Progressive statistics for studies in sports

medicine and exercise science. Med Sci Sports Exerc. 2009;41:3-13.

22. Bosco C, Luhtanen P, Komi PV. A simple method for measurement of mechanical power in

jumping. Eur J Appl Physiol Occup Physiol. 1983;50:273-282.

23. Canavan PK, Vescovi JD. Evaluation of power prediction equations: peak vertical jumping

power in women. Med Sci Sports Exerc. 2004;36:1589-1593.

24. Samozino P, Morin JB, Hintzy F, Belli A. Jumping ability: a theoretical integrative approach. J

Theor Biol. 2010;264:11-18.

25. Markstrom JL, Olsson CJ. Countermovement jump peak force relative to body weight and

jump height as predictors for sprint running performances: (in)homogeneity of track and

field athletes? J Strength Cond Res. 2013;27:944-953.

26. Bosco C, Komi PV. Mechanical characteristics and fiber composition of human leg extensor

muscles. Eur J Appl Physiol Occup Physiol. 1979;41:275-284.

27. Harman EA, Rosenstein MT, Frykman PN, Rosenstein RM. The effects of arms and

countermovement on vertical jumping. Med Sci Sports Exerc. 1990;22:825-833.

28. Morin JB, Samozino P. Interpreting Power-Force-Velocity Profiles for Individualized and

Specific Training Int J Sports Physiol Perform. 2015;In Press

“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 F–v 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