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The study's purpose was to determine the respective influences of the maximal power (Pmax) and the force-velocity (F-v) mechanical profile of the lower limb neuromuscular system on performance in ballistic movements. A theoretical integrative approach was proposed to express ballistic performance as a mathematical function of Pmax and F-v profile. This equation was (i) validated from experimental data obtained on 14 subjects during lower limb ballistic inclined push-offs and (ii) simulated to quantify the respective influence of Pmax and F-v profile on performance. The bias between performances predicted and obtained from experimental measurements was 4%-7%, confirming the validity of the proposed theoretical approach. Simulations showed that ballistic performance was mostly influenced not only by Pmax but also by the balance between force and velocity capabilities as described by the F-v profile. For each individual, there is an optimal F-v profile that maximizes performance, whereas unfavorable F-v balances lead to differences in performance up to 30% for a given Pmax. This optimal F-v profile, which can be accurately determined, depends on some individual characteristics (limb extension range, Pmax) and on the afterload involved in the movement (inertia, inclination). The lower the afterload, the more the optimal F-v profile is oriented toward velocity capabilities and the greater the limitation of performance imposed by the maximal velocity of lower limb extension. High ballistic performances are determined by both maximization of the power output capabilities and optimization of the F-v mechanical profile of the lower limb neuromuscular system.
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Optimal Force–Velocity Profile in Ballistic
Movements—Altius:Citius or Fortius?
PIERRE SAMOZINO
1
, ENRICO REJC
2
, PIETRO ENRICO DI PRAMPERO
2
, ALAIN BELLI
3
,
and JEAN-BENOI
ˆT MORIN
3
1
Laboratory of Exercise Physiology (EA4338), University of Savoy, Le Bourget du Lac, FRANCE;
2
Department of Biomedical Sciences and Technologies, University of Udine, Udine, ITALY; and
3
Laboratory of Exercise Physiology (EA4338), University of Lyon, Saint Etienne, FRANCE
ABSTRACT
SAMOZINO, P., E. REJC, P. E. DI PRAMPERO, A. BELLI, and J.-B. MORIN. Optimal Force–Velocity Profile in Ballistic Move-
ments—Altius:Citius or Fortius? Med. Sci. Sports Exerc., Vol. 44, No. 2, pp. 313–322, 2012. Purpose: The study’s purpose was to
determine the respective influences of the maximal power (P
;
max) and the force–velocity (Fv) mechanical profile of the lower limb
neuromuscular system on performance in ballistic movements. Methods: A theoretical integrative approach was proposed to express
ballistic performance as a mathematical function of P
;
max and Fvprofile. This equation was (i) validated from experimental data
obtained on 14 subjects during lower limb ballistic inclined push-offs and (ii) simulated to quantify the respective influence of P
;
max and
Fvprofile on performance. Results: The bias between performances predicted and obtained from experimental measurements was
4%–7%, confirming the validity of the proposed theoretical approach. Simulations showed that ballistic performance was mostly in-
fluenced not only by P
;
max but also by the balance between force and velocity capabilities as described by the Fvprofile. For each indi-
vidual, there is an optimal Fvprofile that maximizes performance, whereas unfavorable Fvbalances lead to differences in performance up
to 30% for a given P
;
max.ThisoptimalFvprofile, which can be accurately determined, depends on some individual characteristics
(limb extension range, P
;
max)andontheafterloadinvolvedinthemovement(inertia,inclination). The lower the afterload, the more the opti-
mal Fvprofile is oriented toward velocity capabilities and the greater the limitation of performance imposed by the maximal velocity of
lower limb extension. Conclusions:Highballisticperformancesaredeterminedbybothmaximizationofthepoweroutputcapabilitiesand
optimization of the Fvmechanical profile of the lower limb neuromuscular system. Key Words: MAXIMAL POWER, JUMPING
PERFORMANCE, LOWER EXTREMITY EXTENSION, INCLINED PUSH-OFF, EXPLOSIVE STRENGTH, MUSCLE FUNCTION
Ballistic movements, notably jumping, have often
been investigated to better understand the mechani-
cal limits of skeletal muscle function in vivo, be it
in animals (19,23) or in humans (6,9,20). One of the main
questions scientists, coaches, or athletes ask when explor-
ing factors for optimizing ballistic performance is which
mechanical quality of the neuromuscular system is more
important: ‘‘force’’ or ‘‘velocity’ mechanical capability?
Ballistic movements may be defined as maximal move-
ments aiming to accelerate a moving mass as much as pos-
sible, that is, to reach the highest possible velocity in the
shortest time during a push-off. From Newton’s second
law of motion, the velocity reached by the body center of
mass (CM) at the end of a push-off (or takeoff velocity, v
TO
)
directly depends on the mechanical impulse developed in
the movement direction (22,26,42). Because the ability to
develop a high impulse cannot be considered as a mechan-
ical property of the neuromuscular system, the issue is to
identify which mechanical capabilities of the lower limbs
determine the impulse. Developing a high impulse during a
lower limb push-off and, in turn, accelerating body mass as
much as possible have often been assumed to depend on
power capabilities of the neuromuscular system involved in
the movement (14,19,26,29,36,40,43). This explains the
wide interest of sports performance practitioners in im-
proving muscular power (9,10,12,14,27). On this basis,
maximal power output (P
;
max) may be improved by in-
creasing the ability to develop high levels of force at low
velocities (force capabilities or strength) and/or lower levels
of force at high velocities (velocity capabilities) (10,11,27).
The best strategy continues to be an everlasting source of
interest and debate (5,10–12,14,29).
The overall dynamic mechanical capabilities of the lower
limb neuromuscular system have been well described by
inverse linear force–velocity (Fv) and parabolic power–
velocity (Pv)relationshipsduringvarious types of multijoint
Address for correspondence: Pierre Samozino, Ph.D., Laboratoire de Physi-
ologie de l’Exercice, Universite
´de Saint-E
´tienne, Me
´decine du sport et
Myologie - Centre Hospitalier Universitaire Bellevue, 42055 Saint-E
´tienne
Cedex 02, France; E-mail: pierre.samozino@univ-savoie.fr.
Submitted for publication November 2010.
Accepted for publication July 2011.
Supplemental digital content is available for this article. Direct URL
citations appear in the printed text and are provided in the HTML and PDF
versions of this article on the journal’s Web site (www.acsm-msse.org).
0195-9131/12/4402-0313/0
MEDICINE & SCIENCE IN SPORTS & EXERCISE
!
Copyright "2012 by the American College of Sports Medicine
DOI: 10.1249/MSS.0b013e31822d757a
313
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Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
concentric extension movements (3,33,35,40,43). These re-
lationships describe the changes in external force generation
and power output with increasing movement velocity and
may be summarized through three typical variables: the the-
oretical maximal force at null velocity (F
;
0), the P
;
max the
lower limbs can produce over one extension, and the theo-
retical maximal velocity at which lower limbs can extend
during one extension under zero load (v
Y
0). These three pa-
rameters represent the maximal mechanical capabilities of
lower limbs to generate external force, power output, and
extension velocity, respectively. Because they characterize
the mechanical limits of the entire neuromuscular function,
they encompass individual muscle mechanical properties
(e.g., intrinsic Fvand length–tension relationships, rate of
force development), some morphological factors (e.g., cross-
sectional area, fascicle length, pennation angle, tendon prop-
erties), and neural mechanisms (e.g., motor unit recruitment,
firing frequency, motor unit synchronization, intermuscular
coordination) (9). Graphically, F
;
0and v
Y
0correspond to the
force axis and velocity axis intercepts of the linear Fvcurve,
respectively, and P
;
max corresponds to the apex of the para-
bolic Pvrelationship. Under these conditions, the relation-
ship among these three parameters can be described by the
following mathematical equation (41):
!
Pmax ¼
!
F0v
!
0
4½1$
Consequently, two athletes with similar P
;
max could theo-
retically present different Fvmechanical profiles, i.e., dif-
ferent combinations of F
;
0and v
Y
0. The issue is therefore to
determine whether the Fvprofile may influence ballistic
performances independently of P
;
max. In other words, is it
preferable to be ‘strong’’ or ‘‘fast’’ to reach the highest per-
formance in ballistic movements? Such an analysis might
provide greater insight into the relationship between me-
chanical properties of the neuromuscular system and func-
tional performance, either to further explore animal motor
behaviors (19,20) or to program athletic training in humans,
as underlined in recent reviews (10,12,14).
The effects of the Fvmechanical profile on ballistic per-
formance have been experimentally approached only through
studies led in athletes with different training backgrounds
(40,43), through different training protocols (5,7,11,16,27),
or both (4,8). However, in these studies, the various Fv
profiles of athletes were also associated with various P
;
max
values among subjects, making it impossible to identify
the sole effect of the Fvprofile. The influence of force
and velocity capabilities on jumping performance has been
recently addressed through a theoretical integrative approach
mathematically expressing the maximal jump height an indi-
vidual can reach as a function of F
;
0and v
Y
0(37). However,
the observed positive effects of F
;
0and v
Y
0on performance
were not independent from possible effects of P
;
max, the latter
being overlooked.
On the basis of this theoretical approach, the main aim
of this study was to determine the respective influences of
P
;
max and Fvprofile on performance in ballistic lower limb
movements. Moreover, force and velocity contributions to
power output depend on the load involved (10,14). Con-
sequently, the secondary aim of this study was to investigate
whether the effects of the Fvprofile on ballistic per-
formances (if any) depend on the afterloads (additional loads
and/or push-off orientation against gravity) involved in
the movement. To achieve these aims, the aforementioned
theoretical analysis was compared with experimental mea-
surements during jumping.
THEORETICAL BACKGROUND
This section is devoted to an analysis of ballistic per-
formance through maximal jumps at different push-off
angles. The entire lower limb neuromuscular system is
considered as a force generator characterized by an inverse
linear Fvrelationship and a given range of motion. The
maximal jumping performance can be well represented by
the maximal v
TO
(vTOmax)ofthebodyCM.Asdetailedinthe
recent theoretical integrative approach, jumping perfor-
mance can be expressed as a function of some mechanical
characteristics of lower limbs.Inthisapproachmentioned
above (see Samozino et al. [37]), vTOmax can be expressed
as follows:
vTOmax ¼hPO ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Y
F2
0
4Y
v2
0
þ2
hPO
ð
Y
F0jgsin>Þ
sj
Y
F0
2Y
v0
0
@1
A½2$
where gis the gravitational acceleration (9.81 mIs
j2
), >is
the push-off angle with respect to the horizontal (-), h
PO
is the distance covered by the CM during push-off cor-
responding to the extension range of lower limbs (m), and
F
;
0(NIkg
j1
of moving mass) and v
Y
0(mIs
j1
)arethemaxi-
mal force at theoretical null velocity and the theoretical
maximal unloaded velocity of lower limbs, respectively.
The push-off angle >,assumedtobethesameastheaxisof
the force developed, is considered constant over the entire
push-off. In equation 2, the afterload opposing in motion
is taken into account through inertia (i.e., the moving
mass present here in the normalization of F
;
0)andgravity
(g(sin >,i.e.,thecomponentofthegravityopposedtothe
movement).
The Fvmechanical profile of lower limbs can be repre-
sented by the ratio between F
;
0and v
Y
0, i.e., by the slope of
the linear Fvrelationship (S
Fv
) given by the following
equation:
SFv ¼j
Y
F0
Y
v0
½3$
(with the force graphically represented on the vertical axis of
the Fvrelationship).
Thus, the lower the S
Fv
, the steeper the Fvrelation-
ship and the higher the force capabilities compared with
velocity ones (7). Note that S
Fv
and P
;
max are theorized to be
independent.
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Substituting equation 3 in equation 2 gives the following:
vTOmax ¼hPO ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
S2
Fv
4þ2
hPO
ð
Y
F0jgsin>Þ
sþSFv
2
0
@1
A½4$
On the other hand, from equations 1 and 3, F
;
0can be
expressed as a function of P
;
max and S
Fv
:
Y
F0¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j4
Y
PmaxSFv
p½5$
Substituting equation 5 in equation 4 gives the following:
vTOmax ¼hPO ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
S2
Fv
4þ2
hPO
ð2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
Y
PmaxSFv
pjgsin>Þ
sþSFv
2
0
@1
A½6$
Consequently, vTOmax can also be expressed as a func-
tion of P
;
max,S
Fv
, and h
PO
. Equation 6 is true for
h
PO
90,
Y
Pmax 9gsin>2=j4SFv, and SFv Gjgsin>2=4
Y
Pmax
(see appendices, Supplemental Digital Content 1a,
http://links.lww.com/MSS/A114, for details on the com-
putations of these values). In the present study, equation 6
was (i) validated from experimental measurements and (ii)
simulated to analyze the respective influences of P
;
max and
S
Fv
on jumping performance.
METHODS USED IN THE EXPERIMENTAL
VALIDATION
Subjects and experimental protocol. Fourteen sub-
jects (age = 26.3 T4.5 yr, body mass = 83.9 T18.3 kg, stature
= 1.81 T0.07 m) gave their written informed consent to
participate in this study, which was approved by the local
ethical committee and in agreement with the Declaration of
Helsinki. All subjects practiced physical activities including
explosive efforts (e.g., basketball, rugby, soccer); eight of
them were rugby players (four played in the Italian first
league). After a 10-min warm-up and a brief familiarization
with the laboratory equipment, each subject performed two
series of maximal lower limb push-offs: (i) horizontal ex-
tensions with different resistive forces allowing us to deter-
mine Fvrelationships of the lower limbs and (ii) inclined
jumps used to compare experimental performances with
theoretical predictions.
Tests were realized on the Explosive Ergometer
(EXER, see Figure, Supplemental Digital Content 2,
http://links.lww.com/MSS/A115, for a schematic view of
the EXER) consisting of a metal frame supporting one rail
on which a seat, fixed on a carriage, was free to move
(for more details, see Rejc et al. [34]). The total moving
mass (seat + carriage) was 31.6 kg. The main frame could be
inclined up to a maximum angle of 30-with respect to the
horizontal. The subject could therefore accelerate himself or
herself and the carriage seat backward by pushing on two
force plates (LAUMAS PA 300; Parma, Italy) positioned
perpendicular to the rail, the output of which was independent
of the point of application of the force within a wide area. The
velocity of the carriage seat along the direction of motion was
continuously recorded by a wire tachometer (LIKA SGI,
Vicenza, Italy) mounted on the back of the main frame. Force
and velocity analog outputs were sampled at a frequency of
1000 Hz using a data acquisition system (MP100; BIOPAC
Systems, Inc., Goleta, CA). The instantaneous power was cal-
culated from the product of instantaneous force and velocity
values. Data were processed using the AcqKnowledge soft-
ware (BIOPAC Systems, Inc.). An electric motor, positioned
in front of the carriage seat, allowed us to impose known
braking forces, acting along the direction of motion. The mo-
tor, controlled by a personal computer, was linked to the seat
by a chain, its braking action initiating immediately at the
onset of the subject’s push. The braking force of the motor,
ranging from about 200 to 2300 N, was set using a custom-
built LabVIEW program (National Instruments, Austin, TX).
For each test, the subject was seated on the carriage seat,
secured by a safety belt tightened around the shoulders and
abdomen, with the arms on handlebars. The starting posi-
tion, set with feet on the force plates and knees flexed at 90-,
was fixed thanks to adjustable blocks positioned on the rail
of the EXER to prevent the downward movement of the
carriage seat and, in turn, any countermovement.
Fvrelationships of lower limb neuromuscular
system. To determine individual Fvrelationships, each
subject performed horizontal maximal lower limb extension
against seven randomized motor braking forces: 0%, 40%,
80%, 120%, 160%, 200%, and 240% of the subject’s body
weight. The condition without braking force (0% of body
weight) was performed with the motor chain disconnected
from the carriage seat. For each trial, subjects were asked
to extend their lower limbs as fast as possible. Two trials,
separated by 2 min of recovery, were completed at each
braking force. Mean force (F
Y
), velocity (v
Y), and power (P
Y
)
for the best trial of each condition were determined from the
averages of instantaneous values over the entire push-off
phase. The push-off began when the velocity signal in-
creased and ended when the force signal (if takeoff) or the
velocity signal (if no takeoff) fell to zero. As previously
suggested (3,33,43), Fvrelationships were determined by
least squares linear regressions. Because Pvrelationships
are derived from the product of force and velocity, they were
logically described by second-degree polynomial functions.
Fvcurves were extrapolated to obtain F
;
0(then normalized
to total moving mass, i.e., body + carriage seat mass) and v
Y
0,
which correspond to the intercepts of the Fvcurve with the
force and velocity axis, respectively. According to equation
3, S
Fv
was then computed from F
;
0and v
Y
0. Values of P
;
max
(normalized to body + carriage seat mass) were determined
from the first mathematical derivation of Pvregression
equations. Moreover, to test the validity of equation 1, P
;
max
was also computed from this equation (PmaxTH ).
Inclined push-off performance. To validate equa-
tion 6, each subject then performed two inclined maximal
push-offs at three sled angles (>) (10-, 20-, and 30-above
the horizontal) with the motor chain disconnected from
the carriage seat, following the same procedures described
above. v
TO
was determined for each trial as the instantaneous
OPTIMAL FORCE–VELOCITY PROFILE Medicine & Science in Sports & Exercise
d
315
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velocity value when the force signal fell to zero. Push-off
distance (h
PO
) was determined for each subject by integrating
the velocity signal over time during the push-off phase.
Statistical analyses. All data are presented as mean T
SD. For each subject and each sled angle condition, the
highest v
TO
reached in the two trials was compared with
vTOmax computed according to equation 6, from P
;
max,h
PO
,
and S
Fv
.Aftercheckingdistributionsnormalitywiththe
Shapiro–Wilk test, the difference between v
TO
and vTOmax
(bias) was computed and tested using a t-test for paired
samples. To complete this comparison, the absolute dif-
ference between v
TO
and vTOmax (absolute bias) was also
calculated as jðvTOmax jvTOÞvj1
TOj100 (36). Using the same
comparison method, experimental values of P
;
max were
compared with theoretical values (PmaxTH). After checking
the homogeneity of variances, the effect of sled angle was
tested with a one-way ANOVA for repeated measures on
v
TO
and vTOmax .Whenasignificanteffectwasdetected,a
post hoc Newman–Keuls comparison was used to locate
the significant differences. For all statistical analyses, a
Pvalue of 0.05 was accepted as the level of significance.
METHODS USED IN THE SIMULATION STUDY
The relative influences of P
;
max and S
Fv
on vTOmax were
analyzed via equation 6. First, vTOmax changes with S
Fv
were
determined for different P
;
max values at different push-off
angles (>). The range of P
;
max and S
Fv
values used in the
simulations was obtained from data (P
;
max,F
;
0,v
Y
0) previously
reported for human maximal lower limb extensions: P
;
max
from 10 to 40 WIkg
j1
and S
Fv
until to j40 NIsIm
j1
Ikg
j1
(32,33,36,43). The effect of h
PO
on performance, previously
studied and discussed (see Samozino et al. [37]), was not
specifically treated here; h
PO
was set at 0.4 m, which is a
typical value for humans. Then, sensitivity analyses were
performed to assess the respective weight of each variable
plotting relative variations in vTOmax against relative variations
in P
;
max and S
Fv
at different push-off angles (>), each variable
being studied separately.
RESULTS
Validation of the theoretical approach. Individual
Fvand Pvrelationships were well fitted by linear
(r
2
= 0.75–0.99, Pe0.012) and second-degree polynomial
(r
2
= 0.70–1.00, Pe0.024) regressions, respectively. Figure 1
shows these relationships for two typical subjects with dif-
ferent Fvprofiles (i.e., different F
;
0,v
Y
0, and S
Fv
) and dif-
ferent P
;
max capabilities. Mean TSD values of h
PO
,v
Y
0,F
;
0,
P
;
max, and S
Fv
were 0.39 T0.04 m, 2.78 T0.63 mIs
j1
, 24.2 T
2.97 NIkg
j1
(or 17.3 T1.60 NIkg
j1
when normalized to
body + carriage seat mass), 16.34 T2.26 WIkg
j1
(or 11.78 T
1.80 WIkg
j1
when normalized to body + carriage seat
mass), and j9.33 T3.31 NIsIm
j1
Ikg
j1
(or j6.64 T
2.12 NIsIm
j1
Ikg
j1
when normalized to body + carriage seat
mass), respectively. The difference between P
;
max and PmaxTH
was not significant and very low (absolute bias = 1.81% T
0.76%), which shows the validity of equation 1. Mean TSD
values of v
TO
and vTOmax , as well as mean values of absolute
bias, are presented in Table 1. For each push-off angle, v
TO
and vTOmax were not significantly different, and bias was
j0.05 T0.17 mIs
j1
(see Figure, Supplemental Digital
Content 3, http://links.lww.com/MSS/A116, which shows
bias and limits of agreement in a Bland–Altman plot). On
the other hand, the effect of push-off angle was significant
on both v
TO
and vTOmax , with differences between every
condition (Table 1).
Theoretical simulations. As expected, P
;
max positively
affects vTOmax , which is clearly shown in Figure 2 for both
vertical (>= 90-) and horizontal (>=0-) push-offs. The
main original result was the curvilinear changes in vTOmax
with S
Fv
for a given P
;
max (Fig. 2). Such variations highlight
the existence of an optimal S
Fv
(SFvopt ) maximizing vTOmax for
given P
;
max and h
PO
. Moreover, SFvopt values seem to change
slightly as a function of both P
;
max and >values, ranging
FIGURE 1—Typical Fv(left panel) and Pv(right panel) relationships for two subjects with different Fvprofiles (S
Fv
=jF
0
/v
0
) and P
max
values
(gray cross). Subject 1 (open circles) presents a lower P
max
and an Fvprofile more oriented toward force capabilities than subject 2 ( filled circles), who
presents an Fvprofile more oriented toward velocity capabilities.
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from j18 to j6NIsIm
j1
Ikg
j1
for the conditions simulated
in Figure 2. The dependence of SFvopt on P
;
max,>, and h
PO
can be mathematically analyzed: the expression of SFvopt as a
function of these three variables is a real solution canceling
out the first mathematical derivative of vTOmax with respect
to S
Fv
(see appendices, Supplemental Digital Content 1b,
http://links.lww.com/MSS/A114, for detailed computations
of SFvopt ). Whatever the value of P
;
max,SFvopt decreases when
>increases (Fig. 3). For both vertical and horizontal push-
offs, the sensitivity analysis showed that vTOmax is more in-
fluenced by P
;
max than by S
Fv
, at least when the S
Fv
reference
value is equal to SFvopt (Fig. 4). Moreover, the respective
effects of P
;
max and S
Fv
on vTOmax seem to decrease with de-
creasing >(Fig. 4).
DISCUSSION
The original and main findings of this study are that bal-
listic performance of the lower limbs depends on both P
;
max
capabilities and the Fvprofile, with the existence of an
individual optimal Fvprofile corresponding to the best
balance between force and velocity capabilities. This opti-
mal Fvprofile, which can be accurately determined,
depends on some individual characteristics (limb extension
range, P
;
max) and on the afterload involved in the movement
(inertia, inclination). The concept of optimal Fvprofile and
the proposed approach make it possible to clarify some
scientific issues previously discussed about the mechanical
capabilities of lower limbs that determine ballistic perfor-
mance and about the relationships between lower limb
neuromuscular system structure and function. The following
discussion is devoted to detailing these different points.
Validity of the theoretical approach. These findings
were obtained using a theoretical integrative approach based
on fundamental principles of dynamics and on the Fvlinear
model characterizing the dynamic mechanical capabilities of
the neuromuscular system during a lower limb extension.
This linear model, as well as the parabolic Pvrelationship,
has been well supported and experimentally described for
FIGURE 2—Changes in maximal CM v
TO
(v
TOmax
) reached at the end of a lower limb push-off, as a function of the changes in the Fvprofile (S
Fv
) for
different P
max
values and at two push-off angles (>). The h
PO
is fixed here at 0.4 m. For the vertical push-off (>= 90-), the corresponding jump height
(obtained from basic ballistic equations) is presented on the additional yaxis. Open circles represent the v
TOmax
reached for an optimal F–v profile
(S
Fv
opt
).
FIGURE 3—Changes in optimal F–v profile (S
Fvopt
) as a function of
the push-off angle (>) for different P
max
values. The h
PO
is fixed here at
0.4 m.
TABLE 1. Mean TSD of v
TO
obtained with experimental and theoretical approaches,
absolute bias between these two approaches, and t-test comparison results.
>(-)
Experimental Values
(v
TO
(mIs
j1
))
Theoretical Values
(v
TO
max
(mIs
j1
)) t-Test
Absolute
Bias (%)
10 2.45 T0.22 2.43 T0.18 ns 4.40 T4.94
20 2.32 T0.25
a
2.25 T0.16
a
ns 6.56 T5.46
30 2.14 T0.23
ab
2.07 T0.15
ab
ns 5.73 T3.89
a
Significantly different from >= 10-.
b
Significantly different from >= 20-.
ns, nonsignificative difference between experimental and theoretical values.
OPTIMAL FORCE–VELOCITY PROFILE Medicine & Science in Sports & Exercise
d
317
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Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
multijoint movements (3,33,43,44). The linearity of the Fv
relationship, usually presented as hyperbolic for isolated
muscles (17), is explained by the integrative feature of the
model. The force generator and, in turn, its maximal force
(F
;
0), unloaded velocity (v
Y
0), and power (P
;
max) refer here to
the entire in vivo neuromuscular system involving several
muscles with different mixed fiber composition, architec-
tural characteristics, anatomical joint configuration, level
of neural activation, and specific coordination strategies
(7–9,44). The limits of this theoretical approach have been
previously discussed (37), but the significance and accu-
racy of its predictions have not been quantified yet. Besides
validating equation 1 (P
;
max and PmaxTH are very close), the
present results showed no differences between predicted
(vTOmax)andmeasured(v
TO
) values, associated to a low
absolute bias from 4% to 6.6%. This is within the range of
reproducibility indices previously reported for different
variables (performance, velocity, force, or power) mea-
sured during lower limb maximal extensions (3,18). These
results support the validity of the proposed theoretical ap-
proach, which was strengthened by the sensibility of both
predicted and experimental values to changes in push-off
angles. Obviously, the accuracy of equation 6 is enhanced
when muscular properties (P
;
max and S
Fv
)areassessedin
the same conditions (e.g., joints and muscle groups in-
volved, range of motion) under which the actual perfor-
mance is studied, as it was done here on the EXER.
Muscular capabilities determining jumping per-
formance. Among the muscular characteristics determin-
ing jumping performance, P
;
max has the greatest weight.
Although expected, the importance of P
;
max in setting bal-
listic performance needed to be established, as concluded by
Cronin and Sleivert (12) in their recent review: ‘‘power is
only one aspect that affects performance and it is quite likely
that other strength measures may be equally if not more
important for determining the success of certain tasks.’’ The
present results clearly demonstrate this idea. On the other
hand, the dependence of ballistic performances on muscular
power capability brings new insights into the recurrent de-
bate about the role of ‘‘power’’ in impulsive performance,
such as jumping (22,26,42). On the basis of Newton’s sec-
ond law of motion, some authors stated that jumping per-
formance does not depend on the muscular capability to
develop power but rather on the capability to develop a high
impulse (26,42). Even if fundamental principles of dynamics
directly relate mechanical impulse to v
TO
(and in turn jump-
ing performance), the capability to generate impulse does not
represent an intrinsic mechanical property of the lower limb
neuromuscular system, contrary to P
;
max. It is important to
differentiate mechanical outputs (e.g., external force, move-
ment velocity, power output, impulse, mechanical work) from
mechanical capabilities of lower limbs (P
;
max,v
Y
0,F
;
0). On
the one hand, mechanical outputs represent the mechanical
entities that can be externally measured during a movement
and are often used to characterize movement dynamics from
a mechanical point of view. On the other hand, mechanical
capabilities of lower limbs characterize the mechanical lim-
its of the neuromuscular function and refer to the theoretical
maximal values of some mechanical outputs that could be
reached by an individual. The proposed theoretical approach
demonstrates that the ability to develop a high impulse
against the ground and, in turn, the ability to reach maximal
CM velocity at the end of a push-off are highly related to
the P
;
max the lower limbs can produce (over a given exten-
sion range).
That said, the present results show that P
;
max is not the
only muscular property involved in jumping performance.
Indeed, two individuals with the same P
;
max (and the same
h
PO
) may achieve different performances, be it during a
vertical jump or a horizontal push-off (Fig. 2). These dif-
ferences are due to their respective Fvprofiles (S
Fv
), i.e., to
their respective ratios between maximal force (F
;
0) and ve-
locity (v
Y
0) capabilities. For each individual (given his/her
P
;
max and h
PO
), there is an optimal Fvprofile that max-
imizes performance. The more this Fvprofile differs from
the optimal one, the lower the performance in comparison
FIGURE 4—Sensitivity analyses: relative changes in maximal CM v
TO
(v
TOmax
) as a function of the relative variations of P
max
and Fvprofile (S
Fv
) for
two >values. The reference value for P
max
is 25 WIkg
j1
and corresponds to the optimal Fvprofile value for S
Fv
(j14.0 for >=90-and j8.20 for >=0-).
The h
PO
is fixed here at 0.4 m. For S
Fv
, the higher the normalized variation, the lower the value because S
Fv
values are only negative and the more
the Fvprofile tends toward force capabilities.
http://www.acsm-msse.org318 Official Journal of the American College of Sports Medicine
APPLIED SCIENCES
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with the one that could be reached with the same power
capabilities (Fig. 2). The values of S
Fv
observed here (from
j16.8 to j4.9 NIsIm
j1
Ikg
j1
) are consistent with F
;
0and
v
Y
0values previously reported (3,32,33,43). P
;
max and F
;
0
values were slightly lower than those reported during vertical
push-offs (3,32,33), which is likely due to the specific sitting
position imposed by the EXER compared with the totally
extended hip configuration usually tested. Individuals, nota-
bly rugby players, as most of our subjects were, may present
very different Fvprofiles, as shown by coefficients of vari-
ation for S
Fv
of beyond 30% compared with coefficients of
variation below 20% for P
;
max or F
;
0. Most of these different
individual Fvprofiles differ from the optimal ones, thus
characterizing unfavorable balances between force and ve-
locity capabilities. Indeed, individual Fvprofiles observed in
this study ranged from 36% to 104% of the optimal ones
maximizing vertical jumping performance. Simulations of
equation 6 showed that such unfavorable Fvbalances may
be related to differences up to 30% in jump height between
two individuals with similar power capabilities (Figs. 2 and
4). Consequently, we think that the Fvprofile represents a
muscular quality that has to be considered attentively not only
by scientists working on muscle function during maximal
efforts but also by coaches for training purposes.
Effect of afterloads on optimal Fvprofile. The
optimal Fvprofile depends on some individual char-
acteristics (h
PO
,P
;
max) and on the afterload opposing in
motion (inertia, inclination). On the one hand, the Fvpro-
file does affect jumping performances when S
Fv
is expressed
through values normalized to the total moving mass
(NIsIm
j1
Ikg
j1
), which may be body mass, body mass plus
additional loads, or projectile mass. Thus, the interpretation
of Fvprofiles is dependent on the movement considered.
On the other hand, the computation of the optimal Fv
profile also takes account of the total moving mass: SFvopt is a
function of P
;
max, itself expressed relative to moving mass.
Consequently, for a given athlete, the optimal Fvprofile is
not the same for a javelin throw (high P
;
max relative to
moving mass) and for a shot put (low relative P
;
max, see the
different curves in Fig. 3). The optimal Fvprofile also
depends on the push-off angle and more generally on the
magnitude of the gravity component opposing motion (the
lower the push-off angle, the more the optimal Fvprofile is
oriented toward velocity capabilities). Thus, the optimal Fv
profile is not the same when seeking to maximize perfor-
mance during the first push of a sprint or during a vertical
jump; velocity capabilities are more important in the former
case; force capabilities, in the latter. This is in line with the
theoretical framework proposed by Minetti (28) showing
that power output developed during maximal efforts is less
dependent on muscle strength when the exercise does not
involve gravity, as in horizontal extensions. Such horizontal
(or very horizontally inclined) push-offs are thus especially
limited by the velocity capabilities of lower limbs. The
originality of the present theoretical approach is to allow
the accurate determination of the optimal balance between
force and velocity capabilities (through SFvopt ) according to
movement specificities. The subjects tested here presented
an overall unfavorable balance toward velocity capabilities
for vertical jumps (S
Fv
from 36% to 104% of their respective
SFvopt ) and toward force capabilities for horizontal push-offs
(S
Fv
from 66% to 227% of SFvopt ).
Fvprofile and athletic training. Assessing Fv
profiles when seeking to identify the optimal balance be-
tween force and velocity capabilities may be of interest to set
training loads and regimens, as previously proposed using
power–load relationships (10,20,27,38). Values of S
Fv
allow
comparisons among athletes independently from their power
capabilities (which is not possible from only F
;
0and v
Y
0
values) and, thus, to know whether an athlete, as compared
with another one, is characterized by a ‘‘force’’ or a
‘velocity’’ profile (Fig. 1). To the best of our knowledge,
only Bosco (2) proposed an index to compare athletes’ Fv
profiles dividing jump height reached with an additional
load (100% of body mass) by unloaded jump height: the
higher this index, the higher the force capabilities compared
with the velocity ones. However, Bosco’s index does not
allow the orientation of training loads for a given athlete
according to his/her own strengths and weaknesses and to
movement specificities. Therefore, we propose the individ-
ual value of S
Fv
, expressed relatively to SFvopt , as a good and
practical index to characterize the Fvprofile and to design
appropriate training programs. The present results showed
that improving ballistic performance may be achieved
through increasing power capabilities (i.e., shifting Fv
relationships upward and/or to the right [21]) and moving
the Fvprofile as close to the optimal one as possible. Such
changes in the Fvrelationship, notably in its slope, may be
achieved by specific strength training (7,8,21). An athlete
presenting an unfavorable Fvbalance in favor of force
(relatively to his/her optimal profile corresponding to target
movement specificities) should improve his/her velocity
capabilities as a priority by training with maximal efforts
and light (e.g., G30% of one repetition maximum, the latter
being close to F
;
0) or negative loading, which is often called
‘ballistic’’ or ‘‘power’’ training (7,8,11,25,27). On the con-
trary, an athlete with an imbalanced Fvprofile oriented
toward velocity should follow a strength training with heavy
loads (975%–80% of one repetition maximum) to increase
his/her force capabilities as a priority (7,8,27). In both cases,
it is likely that (i) P
;
max will increase and (ii) the Fvprofile
will be optimized (i.e., change toward the optimal one),
partly or totally correcting unfavorable Fvbalances. As
shown in the present study, these two changes would
both result in a higher performance. The mechanisms un-
derlying these changes in Fvrelationships, specific to the
kind of training, include changes in mixed fiber composi-
tion, muscle architecture (hypertrophy, pennation angle),
and neural activation (voluntary activation level, firing
frequency, rate of EMG rise, intermuscular coordina-
tion strategies) (1,7,15,27). These theoretical findings
support previous experimental results about the velocity (or
OPTIMAL FORCE–VELOCITY PROFILE Medicine & Science in Sports & Exercise
d
319
APPLIED SCIENCES
Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
load)-specific changes in performance after training with
light or heavy loads (10,25,27), with the additional origi-
nality of controlling the respective effects of Fvqualities
and P
;
max capabilities.
Fvprofile and optimal load. The proposed approach
brings new insight into the understanding of the relation-
ships between structure and mechanical function of the
lower limb neuromuscular system and, notably, the effect of
specific changes in the Fvrelationship on athletic perfor-
mance. The concept of the Fvprofile could be related to the
maximum dynamic output hypothesis proposed and dis-
cussed by Jaric and Markovic (20) and supported by recent
studies (6,13,30). Their hypothesis states that the optimal
load-maximizing power output in ballistic movements for
physically active individuals corresponds to their own body
weight and inertia (20). They argued that this optimal load
would be related to the particular design of the muscular
system (notably its mechanical properties), itself influenced
by the actual load individuals regularly overcome during
their daily activities. They pointed out, however, that the
different evidences provided needed to be supported by
theoretical frameworks describing the general aspects of the
neuromuscular system’s ability to provide the P
;
max output
against a particular load. This may be done using the theo-
retical approach proposed here. Indeed, the slope of the Fv
relationship and, thus, the ratio between F
;
0and v
Y
0are di-
rectly related to the optimal velocity and force-maximizing
power output and so to the corresponding optimal load.
From Fvand Pvrelationships (Fig. 1), the higher the v
Y
0,
the higher the optimal velocity and the lower the optimal
load. Conversely, high F
;
0values are associated with high
optimal loads. Consequently, the optimal load corresponds
to the mass and inertia of the body only for individuals de-
veloping their individual P
;
max during an unloaded vertical
jump. Because (i) maximal jump height changes with Fv
profile for a given P
;
max (Fig. 2, left panel) and (ii) jump
height and power output (relative to body mass) developed
during a vertical jump are positively related (36), the power
output developed during an unloaded maximal jump de-
pends on the Fvprofile. Consequently, jumping perfor-
mance depends directly on the mean power output developed
during push-off (for a given h
PO
), and the latter can be
maximized by both maximizing P
;
max and optimizing the
Fvprofile. This is illustrated in Figure 5, which shows the
power output developed during a vertical jump (expressed
relatively to P
;
max) according to the Fvprofile expressed
relatively to the optimal one (power output was computed
from equations 6 and 9 of Samozino et al. (36), see appen-
dices for more details, Supplemental Digital Content 1c,
http://links.lww.com/MSS/A114). An optimal Fvprofile,
i.e., an optimal balance between F
;
0and v
Y
0, allows the de-
velopment of P
;
max during an unloaded jump (Fig. 5, left
panel) and thus maximization of jumping performance
(Fig. 5, right panel). Consequently, the body mass represents
the optimal load for individuals with optimal Fvprofiles.
An athlete with an unfavorable Fvbalance develops a
power output lower than P
;
max during an unloaded jump.
Such an athlete would produce P
;
max against a load lower
than body mass if he/she presents a velocity profile and
higher than body mass in the case of a force profile.
The present theoretical framework may help to explain and
understand the possible interindividual differences in opti-
mal load previously observed, discussed, and debated
(6,20,24,30,31,39). The influence of training history re-
cently proposed supports our findings because training
background specificities directly affect the Fvprofile
(8,10,27), which influences the optimal load (39). This is in
line with the maximum dynamic output hypothesis stating
that strength-trained athletes (with high force capabilities)
present optimal loads higher than their body mass (20,39).
In animals and humans, the lower limbs’ neuromuscular
system is likely designed to work optimally against loads
usually supported and mobilized (20,23). Consequently,
animals would naturally present Fvprofiles optimizing
ballistic performance such as horizontal jumps, when these
latter represent their main survival behavior.
FIGURE 5—Left panel: changes in power output developed during a vertical jump (expressed in %P
max
) with changes in Fvprofile (S
Fv
, expressed in
%S
Fvopt
). Right panel: effect of the power output developed during a vertical jump (expressed in %P
max
) on the jump height reached (expressed
relatively to the jump height that could be reached, should the Fvprofile be optimal). Values of P
max
and h
PO
were fixed here at 25 WIkg
j1
and 0.4 m,
respectively.
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Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
CONCLUSIONS
Ballistic performance is mostly determined not only
by the P
;
max lower limbs can generate but also by the Fv
mechanical profile characterizing the ratio between maximal
force capabilities and maximal unloaded extension velocity.
This Fvprofile of lower limbs, independent from power
capabilities, may be optimized to maximize performance.
Altius is neither citius nor fortius but an optimal balance
between the two. This optimal Fvprofile depends on in-
dividual and movement specificities, notably on the after-
load involved (inertia and gravity): the lower the afterload,
the more the optimal Fvprofile will be oriented toward
velocity capabilities. Considering Fvprofile may help better
understand the relationships between neuromuscular system
mechanical properties and functional performance, notably
to optimize sport performance and training. This original me-
chanical quality was put forward by a theoretical integrative
approach and validated here from comparisons between
theoretically predicted performances and experimental mea-
surements during jumping. This approach was discussed here
for lower limb extensions, but the results may be also ap-
plied to other multijoint muscular efforts, such as upper limb
ballistic movements, or more complex movements such as
sprint running.
The authors thank Alberto Botter (Udine Rugby Football Club) for
his help in recruitment of the subjects tested and the subjects for
their ‘‘explosive’’ implication in the protocol.
No funding for this study from the National Institutes of Health,
Wellcome Trust, Howard Hughes Medical Institute, or others was
received.
The authors declare that they have no conflict of interest.
The results of the present study do not constitute endorsement by
the American College of Sports Medicine.
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NOTATION
CM body center of mass
mbody mass or moving mass (kg)
ggravitational acceleration on Earth (9.81 mIs
j2
)
F
Y
mean external force developed over push-off along the push-off axis (relative to moving mass (NIkg
j1
))
v
Ymean CM velocity over push-off along the push-off axis (mIs
j1
)
P
Y
mean power output developed over push-off (relative to moving mass (WIkg
j1
))
F
;
0theoretical maximal value of F
Y
that lower limbs can produce during one extension at a theoretical null v
Y(relative to moving mass (NIkg
j1
))
v
Y
0theoretical maximal value of v
Yat which lower limbs can extend during one extension under the influence of muscle action in a theoretical unloaded condition (mIs
j1
)
P
;
max maximal P
Y
that lower limbs can produce during a push-off (WIkg
j1
)
PmaxTH theoretical value of P
;
max estimated from equation 1 (WIkg
j1
)
h
PO
push-off distance determined by lower limb extension range (m)
v
TO
CM velocity at takeoff (mIs
j1
)
vTOmax maximal v
TO
an individual can reach (mIs
j1
)
>push-off angle with respect to the horizontal (-)
S
Fv
slope of linear Fvrelationship (NIsIm
j1
Ikg
j1
)
SFvopt optimal value of S
Fv
maximizing vTOmax for given values of P
;
max and h
PO
(NIsIm
j1
Ikg
j1
)
http://www.acsm-msse.org322 Official Journal of the American College of Sports Medicine
APPLIED SCIENCES
Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
S
UPPLEMENTAL
D
IGITAL
C
ONTENT
1
APPENDICES
(a) variables values for which the presented equations are true
The variables presented in the equations (
0
F
,
0
v
,
max
,
Fv
S
and
PO
h
) have to be consistent
with push-off dynamics.
Being a distance,
PO
h
has to be a real positive value:
0
PO
h
>
[A1]
In order to takeoff, the mean vertical force developed during push-off (in N) has to be
higher than the body weight component along the axis of movement direction. Hence,
when expressed relative to body mass (in N.kg
-1
), the mean vertical force, and in turn
0
F
, have to be a real positive value higher than the gravitational acceleration
component along the axis of movement direction:
0
sin
α
>Fg [A2]
In the same manner, in order to takeoff, the mean vertical velocity of the CM during
push-off has to be a positive value. Hence,
0
0
v
>
[A3]
From equations [1] and [3],
0
v
can be expressed as a function of
max
and
Fv
S
:
max
0
2
Fv
P
v
S
= [A4]
with
0
Fv
S
<
, since
0
0
>
F and
0
0
v
>
.
Since
0
sin
α
>Fg , and according to equation [1]:
0
max
sin
4
α
>vg
P
[A5]
Substituting equation [A4] in equation [A5] gives:
max
max
sin
2
α
>
Fv
P
g
P
S
[A6]
then,
max
(sin)²
4
α
>
Fv
g
PS [A7]
Since
0
sin
α
>Fg , and according to equation [3]:
0
sin
α
>
Fv
g
Sv [A8]
Substituting equation [A4] in equation [A8], and after reduction, gives:
max
(sin)²
4
α
<
Fv
g
SP [A9]
(b) mathematical expression of
Fv
Sopt
as a function of
max
P
and
PO
h
The optimal slope of F-v relationship (
Fv
Sopt
) is the
Fv
S
value maximizing
max
TO
v. The
mathematical expression of
Fv
Sopt
as a function of
max
and
PO
h
is a real solution of:
max
0
=
TO
Fv
d v
d S [A10]
The first mathematical derivative of
max max
(,,)
TO Fv PO
vPSh
with respect to
Fv
S
is:
max
max 2
max
max
2
max
4
.
²11 2 1
(2 )
24 2
12
4(2)
4




=+++




+



Fv
PO Fv
TO PO
Fv Fv Fv
Fv PO
Fv Fv
PO
P
S
hPS
d v h
SPSgS
d S g h
SPSg
h
[A11]
Equation [A10] has four solutions, of which only one corresponds to real values of
Fv
S
among values for which equation [6] is true:
max
max
,
,
44 32
2
max
2 2
max max max
()
()
(( ) 12 )
33 3
PO
PO
PO PO
Fv
PO PO
P
P
h
h
ggPZ
g
Sopt
PPZ P
hh
hh
+
−−
=− − [A12]
with
(
)
max
1/3
66 352 44 396 88
max max max max
,
()
() 18 54 632 27=− − + +
PO
PO PO PO PO PO
P
h
ZggPPgPP
hh h h h
[A13]
(c) power output developed during a vertical jump as a function of
Fv
S
According to basic ballistic principles, the height reached during a vertical jump (h in m) can
be expressed as a function of the CM vertical take-off velocity (
TO
v
):
2
²
=
TO
v
h
g
[A14]
From equations [6] and [A14], and substituting
TO
v
by
max
TO
v, the maximal jump height an
individual can reach can be expressed as a function of
max
,
Fv
S
and
PO
h
.
On the other hand, the mean power output (
P
in W.kg
-1
) developed during a vertical jump
was expressed as a function of
h
and push-off distance (
PO
h
in m) (Samozino et al., 2008):
2
1()=+
PO
gh
h
Pg
h
[A15]
Consequently, from equations [6], [A14] and [A15],
P
developed during the push-off of a
maximal vertical jump can be expressed as a function of
max
,
Fv
S
and
PO
h
. This allows to
analyze changes in
P
according to changes in
Fv
S
(for a given
max
and
PO
h
, Fig. 5).
SUPPLEMENTAL DIGITAL CONTENT 2
Schematic view of the Explosive Ergometer (EXER). WT wire tachometer, CS carriage seat,
FP force platforms, M electric motor. Rail system (R) and lower frame (LF) are hinged (Hi)
so that R can be tilted upward (see text for further details). To allow the motor to act on the
seat without delays, a constant tension (We = 196 N) is applied to the steel chain (dotted line).
S
UPPLEMENTAL
D
IGITAL
C
ONTENT
3
Averaged v
TO
by the two approaches (m.s
-1
)
1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Differences in v
TO
between the two approaches (m.s
-1
)
-0.4
-0.2
0.0
0.2
0.4
Bias
Bias + 1.96 SD
Bias - 1.96 SD
Bland and Altman plot of differences between values of centre of mass take-off velocity (
TO
v
)
predicted from the proposed theoretical approach and those measured during the experimental
tests for push-off angles of 10° (black filled circles), 20° (grey filled circles) and 30° (open
circles). The solid horizontal line corresponds to the bias (mean differences). Upper and lower
horizontal dotted lines represent the limits of agreement (bias ± 1.96 SD of the differences).
... The jump height was calculated after performing the take-offvelocity procedure [26]. Owing to the fact that the force-velocity relationship of vertical jumps is linear [7,8], the force and velocity data obtained under two different loads (0% and 40% 1RM) were modeled using a least-squares linear regression model to determine the F-v profile, F (V) = F0−aV, where F0 denotes the theoretical maximum force (i.e., the force-intercept), and V0 denotes the theoretical maximum velocity (i.e., the velocity-intercept) corresponding to the slope of the linear F-v relationship (SFv = −F0/V0) [8,29]. The average push-off distance during the 0% and 40% 1RM was used in the analyses. ...
... The jump height was calculated after performing the take-offvelocity procedure [26]. Owing to the fact that the force-velocity relationship of vertical jumps is linear [7,8], the force and velocity data obtained under two different loads (0% and 40% 1RM) were modeled using a least-squares linear regression model to determine the F-v profile, F (V) = F0−aV, where F0 denotes the theoretical maximum force (i.e., the force-intercept), and V0 denotes the theoretical maximum velocity (i.e., the velocity-intercept) corresponding to the slope of the linear F-v relationship (SFv = −F0/V0) [8,29]. The average push-off distance during the 0% and 40% 1RM was used in the analyses. ...
... This study demonstrates that the relative HSQ 1RM is related to the SJ F0 (Fig 1), consistent with a previous study by Rivière et al. [35]. The relative HSQ 1RM reflects the ability of force production at a mean propulsive velocity of 0.33 m/s [36], and F0 reflects the maximum concentric force output that the athlete's lower limbs can theoretically produce during ballistic push-off at null velocity [7,8], indicating that relative HSQ 1RM and F0 are both indices that evaluate the ability of force outputs at low velocities. Therefore, they were considered related in the current study. ...
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Article
Understanding the properties associated with the vertical force–velocity (F–v) profiles is important for maximizing jump performance. The purpose of this study was to evaluate the associations of maximum and reactive strength indicators with the F–v profiles obtained from squat jump (SJ) and countermovement jump (CMJ). On the first day, 20 resistance-trained men underwent measurements for half squat (HSQ) one-repetition maximum (1RM). On the second day, jump performances were measured to calculate the drop jump (DJ) reactive strength index (RSI) and the parameters of F–v profiles (theoretical maximum force [F0], velocity [V0], power [Pmax], and slope of the linear F–v relationship [SFv]) obtained from SJ and CMJ. The DJ RSI was not significantly correlated with any parameter of the vertical F–v profiles, whereas the relative HSQ 1RM was significantly correlated with the SJ F0 ( r = 0.508, p = 0.022), CMJ F0 ( r = 0.499, p = 0.025), SJ SFv ( r = −0.457, p = 0.043), and CMJ Pmax ( r = 0.493, p = 0.027). These results suggest that maximum strength is a more important indicator than reactive strength in improving vertical F–v profiles. Furthermore, the importance of maximum strength may vary depending on whether the practitioner wants to maximize the performance of SJ or CMJ.
... In this context, García-Ramos et al. (2018) [25] recently demonstrated the interest of the force-velocity relationship (FV) to assess the effects of fatigue on the distinct abilities of muscles to produce force, velocity, and power output while performing a multi-joint maximal ballistic task. The linear force-velocity and polynomial power-velocity relationships depend on individual muscle-tendon structural and mechanical properties as well as on the neural activation [26]. These relationships can be summarized by three typical parameters: the theoretical values of the maximal force at zero velocity (F 0) and maximal velocity at zero force (V 0), and the maximal power output (P max). ...
... η2 ¼ 0.06), 14 participants in each sex group were required to obtain a statistical power of 80%. Due to the loss of three participants (two because of back pain and torn muscle during the race and one for noisy EMG recordings), the final group included only 9 female (age: 35 AE 7 years (26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45), body mass: 59.8 AE 8.7 kg, height: 1.66 AE 0.08 m) and 8 male (age: 29 AE 7 years (21-38), body mass: 70.9 AE 6.2 kg, height: 1.76 AE 0.06 m) runners. Two women were in the follicular phase, 4 in the luteal phase and 3 were amenorrhoeic. ...
... Force-velocity relationships were determined by least-squares linear regressions using the average normal force component and velocity at each load. Individual force-velocity slopes were extrapolated to obtain the intercepts corresponding to the theoretical maximal values of "F 0" and "V 0" [26]. Then, the theoretical peak value of the velocity-power polynomial (second-degree) relationships was obtained and noted as "P max" [26]. ...
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Article
The acute and delayed phases of the functional recovery pattern after running exercise have been studied mainly in men. However, it seems that women are less fatigable and/or recover faster than men, at least when tested in isometric condition. After a 20 km graded running race, the influence of sex on the delayed phase of recovery at 2–4 days was studied using a horizontal ballistic force-velocity test. Nine female and height male recreational runners performed maximal concentric push-offs at four load levels a week before the race (PRE), 2 and 4 days (D2 and D4) later. Ground reaction forces and surface electromyographic (EMG) activity from 8 major lower limb muscles were recorded. For each session, the mechanical force-velocity-power profile (i.e. theoretical maximal values of force (F¯¯ 0), velocity (V¯¯¯ 0), and power (P¯¯¯ max)) was computed. Mean EMG activity of each recorded muscle and muscle synergies (three for both men and women) were extracted. Independently of the testing sessions, men and women differed regarding the solicitation of the bi-articular thigh muscles (medial hamstring muscles and rectus femoris). At mid-push-off, female made use of more evenly distributed lower limb muscle activities than men. No fatigue effect was found for both sexes when looking at the mean ground reaction forces. However, the force-velocity profile varied by sex throughout the recovery: only men showed a decrease of both V¯¯¯ 0 (p < 0.05) and P¯¯¯ max (p < 0.01) at D2 compared to PRE. Vastus medialis activity was reduced for both men and women up to D4, but only male synergies were impacted at D2: the center of activity of the first and second synergies was reached later. This study suggests that women could recover earlier in a dynamic multi-joint task and that sex-specific organization of muscle synergies may have contributed to their different recovery times after such a race.
... To this end, we generated a range of theoretical simulations of FvP outputs based on a validated biomechanical model of jumping. 14,17,18,24 Our aim was to quantify the range in error in kinetic output variables (F 0 , v 0 , P max , and S Fv ) that might arise from noise in the 2 main kinematic input measurements (h po and h, their magnitude drawn from previous studies). Note that if h po and h are the 2 main inputs (in addition to body mass), 24 they represent indices of procedural rigor independent from the FvP profile concept itself: h po variability informs quality of task standardization, and h variability is associated with biological variation in performance, including variability caused by limited familiarization or submaximal intent. ...
... The first simulated test was considered "perfect" (Fv curve r 2 = 1): h obtained for each load was estimated from individual Fv relationships, body mass, and h po values. 17 In the second simulated test, random errors were included in h po (simulating errors in squat depth standardization) and h for each loading condition (simulating biological variability) with different noise magnitudes: averaged raw error over all virtual subjects from 0 to 4.5 cm for h po and h (ie, coefficient of variation from 0% to ∼13%). From these h and h po values, push-off averaged force, velocity, and power were estimated and used to determine individual Fv relationships of the Task-inexperienced participants. ...
Full-text available
Article
When poor reliability of “output” variables is reported, it can be difficult to discern whether blame lies with the measurement (ie, the inputs) or the overarching concept. This commentary addresses this issue, using the force-velocity-power (FvP) profile in jumping to illustrate the interplay between concept, method, and measurement reliability. While FvP testing has risen in popularity and accessibility, some studies have challenged the reliability and subsequent utility of the concept itself without clearly considering the potential for imprecise procedures to impact reliability measures. To this end, simulations based on virtual athletes confirmed that push-off distance and jump-height variability should be <4% to 5% to guarantee well-fitted force–velocity relationships and acceptable typical error (<10%) in FvP outputs, which was in line with previous experimental findings. Thus, while arguably acceptable in isolation, the 5% to 10% variability in push-off distance or jump height reported in the critiquing studies suggests that their methods were not reliable enough (lack of familiarization, inaccurate procedures, or submaximal efforts) to infer underpinning force-production capacities. Instead of challenging only the concept of FvP relationship testing, an alternative conclusion should have considered the context in which the results were observed: If procedures’ and/or tasks’ execution is too variable, FvP outputs will be unreliable. As for some other neuromuscular or physiological testing, the FvP relationship, which magnifies measurement errors, is unreliable when the input measurements or testing procedures are inaccurate independently from the method or concept used. Field “simple” methods require the same methodological rigor as “lab” methods to obtain reliable output data.
... However, the definition of the optimal profile, especially for different motor tasks such as singlejoint movements, represents a challenging task. Some indices suggest that the optimal F-v profile depends highly on the movement task (Samozino et al., 2012). Besides the necessity to describe mechanical capacity of muscles, particularly important could be the information regarding potential discrepancies between optimal F-v profile of the task and individual F-v profile indicating the imbalances in external mechanics. ...
... With this in mind, it is not surprising that F-v profiles have attracted considerable interest in the last decade among researchers and practitioners who aimed to optimize and suit the measurement profile to various motor tasks. In particular, high linearity of the F-v relationship has been observed in multijoint tasks such as vertical jumps, squats or bench press (Samozino et al., 2008;Samozino et al., 2012;Jaric, 2015;García-Ramos et al., 2016;Jiménez-Reyes et al., 2016;García-Ramos et al., 2021). On the other hand, only a few studies have considered the F-v or torque-velocity profiles (i.e., reporting maximal theoretical values at zero force/torque or zero velocity and the slope of relationship) of single-joint movements isokinetic conditions (Lemaire et al., 2014;Grbic et al., 2017a;Janicijevic et al., 2019). ...
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Article
Over the past decade, force-velocity (F-v) profiling has emerged as a promising tool for assessing neuromuscular capacity to design individually tailored interventions in diverse populations. To date, a limited number of studies have addressed the optimization of the linear method for measuring F-v profiles of single-joint isokinetic movements. We aimed to simplify the measurement of knee extension (KE) and knee flexion (KF) isokinetic tasks by evaluating the most appropriate combination of two velocities (i.e., the 2-point method). Twenty-two healthy participants (11 males and 11 females) were included in the study. Isokinetic peak torque was measured at nine angular velocities (30-60-90-120-150-180-210-240-300°/s) and under isometric conditions (at 150° and 120° of KF for KE, and KF, respectively). Maximal theoretical force (F0), maximal theoretical velocity (v0), slope of the relationship (Sfv) and maximal theoretical power (Pmax) were derived from the linear F-v profiles of KE and KF and compared between the 9-point method and all possible combinations (36 in total) of the 2-point methods. The F-v profiles obtained from nine points were linear for KE (R2 = 0.95; 95% CI = 0.94–0.96) and KF (R2 = 0.93; 95% CI = 0.90–0.95), with F0 underestimating isometric force. Further analyses revealed great to excellent validity (range: ICCs = 0.89–0.99; CV = 2.54%–4.34%) and trivial systematic error (range: ES = −0.11–0.24) of the KE 2-point method when force from distant velocities (30°/s, 60°/s or 90°/s combined with 210°/s, 240°/s or 300°/s) was used. Similarly, great to excellent validity and trivial systematic error of the KF 2-point method for F0 and Pmax (range: ICC = 0.90–0.96; CV = 2.94%–6.38%; ES = −0.07–0.14) were observed when using the previously described combinations of velocities. These results suggest that practitioners should consider using more distant velocities when performing simplified isokinetic 2-point single-joint F-v profiling. Furthermore, the F-v profile has the potential to differentiate between the mechanical properties of knee extensors and flexors and could therefore serve as a potential descriptor of performance.
... The F-V profile of athletes is variable depending on the sport and on the individual capabilities 17 . It has also been observed that acceleration-and sprint-related variables (e.g., maximal speed or accelerations) vary according to contextual variables such as the playing position. ...
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Article
The aim of this study was to analyse the differences in the A–S profile of elite football players induced by playing position and the microcycle day. Players belonged to a second division club in the Spanish La Liga competition. They were classified into five playing positions: central defenders (CD), full backs (FB), midfielders (MF), wide midfielders (WMF) and forwards (FW). Microcycle days were categorised according to the days until matchday (MD, MD-1, MD-2, MD-3, MD-4 and MD-5). Data was collected along six microcycles, including one match per microcycle. The variables analysed were: maximal theoretical acceleration (A0), maximal theoretical speed (S0), maximal acceleration (ACCmax), maximal speed (Smax) and A–S slope (ASslope). Significant differences were found within positions and microcycle day for all variables (p < 0.05). Match day (MD) showed greater values than the training sessions in A0, ACCmax and Smax (p < 0.05). The highest values for variables associated with acceleration capabilities were found in CD on MD, whereas speed variables were higher in WMF. MD-2 showed the lowest values in all variables except for ASslope. Maximal acceleration and sprint abilities are therefore affected by playing position. Wide positions showed the highest speed capacity, and CD presented a likely acceleration profile. Higher values for all variables concerning the microcycle day, were achieved on MD, and were not reproduced during training with the consequent injury risk and performance decrease it takes.
... ) and the Force-Velocity profile during a ballistic movement. The results were innovative since through the use of the proper equations and, in combination with the force velocity slope (Sfv= -(F0/V0)), a coach can construct a training plan which will not only increase the maximum power, but also the force, the velocity and the overall performance (Samozino et. al., 2011). More recently, investigations have used the load-velocity device in a pull-up exercise. In research in which resistance-trained men participated, great correlation was observed between forcevelocity, power-velocity (R^2= 0.95, R^2= 0.96), 1RM-F0 and V0-Pmax (Lopez et. al. 2017). However, in contrast to the previous study, which did not ...
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Thesis
The purpose of this research is to evaluate differences between advance and elite boulder climbers during a prone pull-up test and to determine an optimal load in which the peak power production occurs. In total 6 boulder climbers were recruited (3 advance, 3 elite) and they performed two prone pull-ups in different incremental loads (0%,30%,45%,60%,70) relative to their body mass. The GYMAWARE VBT was used for the data collection and it had been fixed at the back loop of the climbing harness in the area of the lumbar spine. Prior to the research all the participants performed the same 30-minute warm up and during the test all the athletes had the same 3-minute passive rest between the sets. Peak propulsive velocity and peak propulsive power was collected from the GYMAWARE VBT. Intraclass Correlation Coefficient (ICC) and Coefficient of Variation (CV) were calculated through SPSS software in order to evaluate the reliability of the test. Mean propulsive peak velocity (MPV), mean propulsive peak power (MPP), load velocity slope (LVs), force velocity slope (FVs), theoretical max power (Pmax), F0 and V0 differences between advance and elite boulderers were calculated through the independent sample T-test which ran into JASP. Significant differences in MPV, MPP, Pmax, LVs, FVs and V0 were hypothesised to be found. Furthermore, the 71%-1RM was expected to be the optimal load in which the peak power production occurs. The results showed elite boulderers to be significantly different (p<.05) in their MPV, MPP, Pmax, LVs and the effect size was large between the two groups for all the variables (η^2> .25). In conclusion, elite boulderers were noticed to pull up with higher power than the advance individuals and peak power production was observed to happen between 55%-61%1RM.
... According to the literature [1] and [2], we learn that the conventional FVP model is only related to the velocity and combined external forces. Based on this model we combined the method of finding wind force based on temperature, altitude, wind speed and wind direction in thermal physics to establish an EVP model related to external conditions such as weather changes, which can constantly self-correct the equation between position and force on the track according to the actual movement of athletes, and thus determine the potential influence of weather conditions. ...
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Article
As one of the world's favorite extreme sports, bicycle racing gives people a physical workout and is in line with today's global community's advocacy of low carbon. The individual time trial and team time trial in bicycle racing is a great challenge for athletes. In this sport, different athletes have different power curves, and athletes have to adjust their power curves according to the actual situation during the ride. And when and where athletes adjust their power usually determines whether they can win the race or not. Therefore, in order to find the best power adjustment strategy, we build a mathematical model for determining the relationship between rider's position on the track and rider's power, as well as the power profiles of athletes on specific tracks, and try to apply it on any type of riders.
... Increasing additional load during jumping implicitly changes the total power output by increasing force and decreasing velocity [13]. Moreover, CMJ load increases concentric phase duration, net impulse, and mean force during the propulsive and braking phase of the jump, among other kinematic and kinetic variables [1,14]. ...
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Article
This study aimed to investigate the effect of additional loads and sex on countermovement jump (CMJ) joint kinetics during the entire take-off impulse in males and females. Twelve female and 13 male sport students performed vertical countermovement jumps without and with additional loads up to +80% of body mass using a straight barbell. Ground reaction forces and body kinematics were collected simultaneously. A significant increase was found for peak ankle power, whereas knee and hip peak power decreased significantly as additional load increased in both males and females. Joint work increased in each joint as additional load increased, although significance was observed only in the hip joint. Peak power of each joint (22–47%) and total hip work (61%) were significantly higher for males than females. Relative joint contributions to total joint work (“joint work contribution”) remained stable as additional loads increased, whereas meaningful differences were found in the magnitudes of joint work contribution between males and females. CMJ joint kinetics and joint work contributions were distinctly influenced by additional load and sex. Hence, these differences should be considered when prescribing loaded jumps for training or testing.
... These movements require high velocity rather than high maximal strength in the upper body, as the ability of muscles to produce force decreases with increasing movement velocity (Young, 2006;Cormie et al., 2010). Establishing the force-velocity profile for a specific exercise enables the highest mechanical power output and the intensity (i.e., load and velocity) at which it is produced to be characterized on an individual basis (Wilson et al., 1993;Cronin et al., 2001a;Samozino et al., 2012;Jaric, 2015). Depending on the exercise type, equipment used, training status, and muscle groups elicited, power output is shown to be the greatest at intensities ranging between 30-70% of one repetition maximum (RM) (Wilson et al., 1993;Cronin et al., 2001b;Sakamoto et al., 2018;Đurić et al., 2021). ...
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Article
The aims of this study were to compare power output during a bench press throw (BPT) executed with (BPT bounce) and without (BPT) the barbell bounce technique, and examine the effect of cueing different barbell descent velocities on BPT power output in resistance-trained males. In total, 27 males (age 23.1 ± 2.1 years; body mass 79.4 ± 7.4 kg; height 178.8 ± 5.5 cm; and 4.6 ± 1.9 years of resistance training experience) were recruited and attended one familiarization session and two experimental sessions (EXP 1 and EXP 2). The force-velocity profile during maximal BPT and BPT bounce (randomized order) under different loads (30-60 kg) was established (EXP 1), and the effect of varying external barbell descent velocity cues "slow, medium, and as fast as possible" (i.e., "fast") on the power output for each technique (BPT and BPT bounce) was examined (EXP 2). Comparing two BPT techniques (EXP 1), BPT bounce demonstrated 7.9-14.1% greater average power (p ≤ 0.001, ES = 0.48-0.90), 6.5-12.1% greater average velocity (p ≤ 0.001, ES = 0.48-0.91), and 11.9-31.3% shorter time to peak power (p ≤ 0.001-0.05, ES = 0.33-0.83) across the loads 30-60 kg than BPT. The cueing condition "fast" (EXP 2) resulted in greater power outcomes for both BPT and BPT bounce than "slow." No statistically significant differences in any of the power outcomes were observed between "medium" and "slow" cuing conditions for BPT (p = 0.097-1.000), whereas BPT bounce demonstrated increased average power and velocity under the "medium" cuing condition, compared to "slow" (p = 0.006-0.007, ES = 0.25-0.28). No statistically significant differences were observed in barbell throw height comparing BPT and BPT bounce under each cuing condition (p = 0.225-1.000). Overall, results indicate that both bouncing the barbell and emphasizing barbell descent velocity be considered to improve upper body power in athlete and non-athlete resistance-training programs.
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This series of reviews focuses on the most important neuromuscular function in many sport performances: the ability to generate maximal muscular power. Part 1, published in an earlier issue of Sports Medicine, focused on the factors that affect maximal power production while part 2 explores the practical application of these findings by reviewing the scientific literature relevant to the development of training programmes that most effectively enhance maximal power production. The ability to generate maximal power during complex motor skills is of paramount importance to successful athletic performance across many sports. A crucial issue faced by scientists and coaches is the development of effective and efficient training programmes that improve maximal power production in dynamic, multi-joint movements. Such training is referred to as 'power training' for the purposes of this review. Although further research is required in order to gain a deeper understanding of the optimal training techniques for maximizing power in complex, sports-specific movements and the precise mechanisms underlying adaptation, several key conclusions can be drawn from this review. First, a fundamental relationship exists between strength and power, which dictates that an individual cannot possess a high level of power without first being relatively strong. Thus, enhancing and maintaining maximal strength is essential when considering the long-term development of power. Second, consideration of movement pattern, load and velocity specificity is essential when designing power training programmes. Ballistic, plyometric and weightlifting exercises can be used effectively as primary exercises within a power training programme that enhances maximal power. The loads applied to these exercises will depend on the specific requirements of each particular sport and the type of movement being trained. The use of ballistic exercises with loads ranging from 0% to 50% of one-repetition maximum (1RM) and/or weightlifting exercises performed with loads ranging from 50% to 90% of 1RM appears to be the most potent loading stimulus for improving maximal power in complex movements. Furthermore, plyometric exercises should involve stretch rates as well as stretch loads that are similar to those encountered in each specific sport and involve little to no external resistance. These loading conditions allow for superior transfer to performance because they require similar movement velocities to those typically encountered in sport. Third, it is vital to consider the individual athlete's window of adaptation (i.e. the magnitude of potential for improvement) for each neuromuscular factor contributing to maximal power production when developing an effective and efficient power training programme. A training programme that focuses on the least developed factor contributing to maximal power will prompt the greatest neuromuscular adaptations and therefore result in superior performance improvements for that individual. Finally, a key consideration for the long-term development of an athlete's maximal power production capacity is the need for an integration of numerous power training techniques. This integration allows for variation within power meso-/micro-cycles while still maintaining specificity, which is theorized to lead to the greatest long-term improvement in maximal power.
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This series of reviews focuses on the most important neuromuscular function in many sport performances, the ability to generate maximal muscular power. Part 1 focuses on the factors that affect maximal power production, while part 2, which will follow in a forthcoming edition of Sports Medicine, explores the practical application of these findings by reviewing the scientific literature relevant to the development of training programmes that most effectively enhance maximal power production. The ability of the neuromuscular system to generate maximal power is affected by a range of interrelated factors. Maximal muscular power is defined and limited by the force-velocity relationship and affected by the length-tension relationship. The ability to generate maximal power is influenced by the type of muscle action involved and, in particular, the time available to develop force, storage and utilization of elastic energy, interactions of contractile and elastic elements, potentiation of contractile and elastic filaments as well as stretch reflexes. Furthermore, maximal power production is influenced by morphological factors including fibre type contribution to whole muscle area, muscle architectural features and tendon properties as well as neural factors including motor unit recruitment, firing frequency, synchronization and inter-muscular coordination. In addition, acute changes in the muscle environment (i.e. alterations resulting from fatigue, changes in hormone milieu and muscle temperature) impact the ability to generate maximal power. Resistance training has been shown to impact each of these neuromuscular factors in quite specific ways. Therefore, an understanding of the biological basis of maximal power production is essential for developing training programmes that effectively enhance maximal power production in the human.
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Although the effect of external load on the mechanical output of individual muscle has been well documented, the literature still provides conflicting evidence regarding whether the optimum loading (L(opt)) for exerting the maximum muscle power output (MPO) could be different for individuals with different levels of strength and power. The aim of this study was to explore the effect of training history on L(opt) that maximizes MPO during the 6-s maximal cycling sprint test. Forty healthy young males (strength-and speed-trained athletes, and physically active and sedentary non-athletes) were tested on maximum strength, and on peak MPO when loaded 5-12% of body weight (BW). As expected, the strength trained and sedentary participants, respectively, revealed the highest and lowest strengths and MPO (p < 0.001). However, the main finding was a significant across-group difference in L(opt) (p < 0.001) revealing the values 9.7% (for strength trained), 9.2% (speed trained), 8.7% (active), and 8.0% of BW (sedentary individuals). This suggests that the effects of external loading on maximum MPO in complex functional movements could be training history dependent. In addition to revealing a sensitivity of the 6-s maximal cycling sprint tests (and, perhaps, other maximum cycling tests), the results suggest that the external loading in routine MPO tests should not be solely adjusted to a fixed percentage of subject's BW (as routinely done in standard tests), but also to their training history. The same phenomenon remains to be evaluated in a number of other routine tests of MPO and other maximum performance tasks.
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We examined the effects of jump training with negative (-30% of the subject's body weight (BW)) VS. positive loading (+30% BW) on the mechanical behaviour of leg extensor muscles. 32 men were divided into control (CG), negative loading (NLG), or positive loading training group (PLG). Both training groups performed maximal effort countermovement jumps (CMJ) over a 7-week training period. The impact of training on the mechanical behaviour of leg extensor muscles was assessed through CMJ performed with external loads ranging from -30% BW to +30% BW. Both training groups showed significant ( P≤0.013) increase in BW CMJ height (NLG: 9%, effect size (ES)=0.85, VS. PLG: 3.4%, ES=0.31), peak jumping velocity ( V(peak); NLG: 4.1%; ES=0.80, P=0.011, VS. PLG: 1.4%, ES=0.24; P=0.017), and depth of the countermovement (Δ H(ecc); NLG: 20%; ES=-1.64, P=0.004, VS. PLG: 11.4%; ES=-0.86, P=0.015). Although the increase in both the V(peak) and Δ H(ecc) were expected to reduce the recorded ground reaction force, the indices of force- and power-production characteristics of CMJ remained unchanged. Finally, NLG (but not PLG) suggested load-specific improvement in the movement kinematic and kinetic patterns. Overall, the observed results revealed a rather novel finding regarding the effectiveness of negative loading in enhancing CMJ performance which could be of potential importance for further development of routine training protocols. Although the involved biomechanical and neuromuscular mechanisms need further exploration, the improved performance could be partly based on an altered jumping pattern that utilizes an enhanced ability of leg extensors to provide kinetic and power output during the concentric jump phase.