Methods of Power-Force-Velocity Profiling During Sprint Running: A Narrative Review

Abstract

The ability of the human body to generate maximal power is linked to a host of performance outcomes and sporting success. Power-force-velocity relationships characterize limits of the neuromuscular system to produce power, and their measurement has been a common topic in research for the past century. Unfortunately, the narrative of the available literature is complex, with development occurring across a variety of methods and technology. This review focuses on the different equipment and methods used to determine mechanical characteristics of maximal exertion human sprinting. Stationary cycle ergometers have been the most common mode of assessment to date, followed by specialized treadmills used to profile the mechanical outputs of the limbs during sprint running. The most recent methods use complex multiple-force plate lengths in-ground to create a composite profile of over-ground sprint running kinetics across repeated sprints, and macroscopic inverse dynamic approaches to model mechanical variables

Full text

REVIEW ARTICLE
Methods of Power-Force-Velocity Profiling During Sprint
Running: A Narrative Review
Matt R. Cross
1
•Matt Brughelli
1
•Pierre Samozino
2
•Jean-Benoit Morin
1,3
ÓSpringer International Publishing Switzerland 2016
Abstract The ability of the human body to generate
maximal power is linked to a host of performance out-
comes and sporting success. Power-force-velocity rela-
tionships characterize limits of the neuromuscular system
to produce power, and their measurement has been a
common topic in research for the past century. Unfortu-
nately, the narrative of the available literature is complex,
with development occurring across a variety of methods
and technology. This review focuses on the different
equipment and methods used to determine mechanical
characteristics of maximal exertion human sprinting. Sta-
tionary cycle ergometers have been the most common
mode of assessment to date, followed by specialized
treadmills used to profile the mechanical outputs of the
limbs during sprint running. The most recent methods use
complex multiple-force plate lengths in-ground to create a
composite profile of over-ground sprint running kinetics
across repeated sprints, and macroscopic inverse dynamic
approaches to model mechanical variables during over-
ground sprinting from simple time-distance measures dur-
ing a single sprint. This review outlines these approaches
chronologically, with particular emphasis on the compu-
tational theory developed and how this has shaped subse-
quent methodological approaches. Furthermore, training
applications are presented, with emphasis on the theory
underlying the assessment of optimal loading conditions
for power production during resisted sprinting. Future
implications for research, based on past and present
methodological limitations, are also presented. It is our aim
that this review will assist in the understanding of the
convoluted literature surrounding mechanical sprint pro-
filing, and consequently improve the implementation of
such methods in future research and practice.
Key Points
Power-force-velocity relationships can be assessed
during maximal sprinting using a variety of
methods and technologies — from multiple trials
performed on friction-braked cycle ergometers
and specialised treadmills, to ‘simplified’
techniques employing a single over ground trial
measured via timing gates, radar, or even cellular
devices.
Although the direct development of mechanical
profiling spans almost a century, the rapid
expansion of these and other methods in recent years
has led to limited data on modern equipment.
While there is growing evidence to support the value
of these techniques, future studies should look to
collect normative data on highly trained cohorts and
examine their usefulness in orienting and assessing
training outcomes.
&Matt R. Cross
mcross@aut.ac.nz
1
Sports Performance Research Institute New Zealand
(SPRINZ), Auckland University of Technology, Auckland,
New Zealand
2
Inter-University Laboratory of Human Movement Biology,
University Savoie Mont Blanc, Le Bourget-du-Lac, France
3
Universite
´Co
ˆte d’Azur, LAMHESS, Nice, France
123
Sports Med
DOI 10.1007/s40279-016-0653-3

1 Background
The ability of skeletal muscle to generate force and the
maximal rate of movement is described in the force-ve-
locity (Fv) relationship. The relationship postulates that for
a given constant level of muscular activation, increasing
shortening velocity progressively decreases the force pro-
duced by the neuromuscular system [1]. Mechanical power
output (i.e. the rate of performing mechanical work), in this
instance, is defined as the product of force and velocity. As
the maximal abilities of skeletal muscle to generate both
force and velocity are intertwined, the Fv relationship
characterizes the ability to produce and maximize power.
The term maximal power (Pmax ) describes the peak com-
bination of velocity and force achieved in a given muscular
contraction, or movement task [2–4]. Fv and power-ve-
locity (Pv) relationships (i.e. PFv) have been examined,
in vitro and in vivo, to give insight into the mechanical
determinants of performance and further our understanding
of movement.
1.1 History of Force-Velocity Profiling
The first studies to report concepts of force, velocity and
maximal work were based on theoretical methods derived
from hydraulicians, where fluid within the muscle has a
certain velocity, and any work performed (effort) is pro-
portional to the square of velocity (v)[5]. The first
experimental studies in this area [6,7] showed that skeletal
muscle performed similarly to other mechanical systems
where increasing velocity resulted in decreasing work, and
this work-time relationship corresponded to the force-time
relationship [8]. A decade after these studies, an expo-
nential function was developed from in vitro experimen-
tation [9,10], after which Hill [1] derived the well-known
hyperbolic equation (Table 1; Eq. 1) which has been
widely used in power-based sprint-cycling research
[11,12]. While Hill’s rectangular hyperbola accurately fits
the data provided by many single-joint actions across dif-
fering testing procedures, this relationship does not
describe external force production occurring during multi-
joint actions [13,14].
There are several modalities through which these char-
acteristics are assessed in in vivo movement tasks: (1)
control and manipulation of the force imposed on the
movement, and measurement of velocity (isotonic) [15];
(2) control and manipulation of movement velocity and the
subsequent measurement of force (isokinetic) [16]; and (3)
control and manipulation of the external constraints (inertia
and/or weight) and measurement of force and/or velocity
(isoinertial) [17]. Regardless of the testing conditions, the
Table 1 Development of computation methods for mechanical sprint profiling using multiple- and single-cycle ergometer methods
Study and mechanical profiling type Formula Equation number
Hill [1]
Hyperbolic relationship equation (Fv)FþaðÞVþbðÞ¼bF0þaðÞ¼aV0þbðÞ¼constant [1]
Vandewalle et al. [41]
Least square method of theoretical mechanical
variables from multiple sprint method Vmax ¼abF Vmax ¼V01F
F0

F¼F01Vmax
V0
 [2]
Calculation of peak power from linear force-velocity
relationship
Pmax ¼0:5F00:5V0¼0:25F0V0¼F0V0
ðÞ=4 [3]
Lakomy [43]
Correction of peak-power for inclusion of acceleration Fcorr ¼Facc þFP
rev ¼FcorrVrev [4]
Vandewalle et al. [118]
Determination of the slope of the force velocity
relationship
SFv ¼F0=V0[5]
Driss and Vandewalle [38]
Relationship between velocity and time during a single
maximal sprint V¼V01F
F0

1et=u

u¼2pyv0I
9:81F0rV¼Vpeak 1et=u

[6]
Calculation of mechanical variables from a single
maximal sprint Fcorr ¼F01V
V0

¼F0F0
V0

V¼F
F0þ1F
F0

et=u
hi
F0
P¼VFcorr ¼F
F0þ1F
F0

et=u
hi
1F
F0

ð1et=uÞ
hi
F0V0
[7]
[8]
Fforce, Aor aparameter corresponding to force, Vvelocity, Bor bparameter corresponding to velocity, ttime, F
0
maximum isometric force at
null velocity, V
0
maximal velocity at null force, Vmax peak velocity reached at each braking load (F), V0and F0the intercepts of the velocity and
force axis, respectively, Pmax peak of the parabolic power-load curve, Facc force required to accelerate the flywheel of a cycle ergometer, Prev and
Vrev power and velocity averaged per crank revolution of a cycle ergometer, respectively, SFv slope of the force velocity graph, Vpedal rate, T
crank torque corresponding to v,uthe time constant, ygear ratio of the cycle ergometer, v
0
V0=60, rradius of the cycle ergometer flywheel, I
moment of inertia, F0expressed in kg
M. R. Cross et al.
123

effort presented is maximal given that the goal is to
determine the mechanical limit of the neuromuscular sys-
tem. Isoinertial experiments are most common as they best
represent the natural movement patterns found in sporting
contexts, and generally represent a less costly and complex
alternative to isokinetic and isotonic modalities. Typically,
in an isoinertial experiment external loading conditions are
manipulated and the responses of the dependent variables
of force and/or velocity are measured across single or
multiple trials.
1.2 Characterisation of Mechanical Capacity
in Multi-Joint Tasks
While non-linear relationships are typically observed in Fv
profiles with individual joints or muscle fibres [10], multi-
joint tasks appear to present quasi-linear relationships.
Notably, the Fv relationships observed in multiple joint
movements are a product of complex interactions between
muscular coordination characteristics, activation patterns,
the anatomy of joints, and the orientation of moments
occurring (among others) (for an extensive recent review see
Jaric [14]). While neural mechanisms were considered to
primarily cause these observations [15,18,19], recent evi-
dence suggests segmental dynamics may instead be the main
determinant of linear Fv profiles in these tasks, with each
joint progressively impeding muscular production of force
with increasing velocity, thus decreasing external force
[13,20]. Inverse linear Fv and parabolic power-velocity (Pv)
relationships have subsequently been used in recent practice
to describe the mechanical capabilities of the neuromuscular
system during a range of multi-joint lower-limb movements
(for a detailed review of these methods see Soriano et al.
[21]): primarily variations on jumping and similar acyclic
extensions of the lower limbs [15,22–29].
Changes in external force production across varying
movement velocities are described by PFv relationships,
and are most commonly displayed by the following three
variables in literature: the theoretical maximum force the
system can produce at zero velocity (F0); the theoretical
maximum velocity at which the system can contract/extend
at zero force (v0); and the Pmax the system can produce
(either during cyclic or acyclic movements). F0and v0
represent the y and x intercepts of the linear regression,
respectively. Pmax corresponds to the apex of the parabolic
Pv relationship and can be computed directly from F0and
v0for linear Fv relationships: Pmax ¼F0v0
ðÞ=4 (see
Table 1; Eq. 5) [28,30]. Principally, these variables char-
acterize the maximal mechanical abilities of the total sys-
tem (depending on the movement and definition used in
each circumstance) pertaining to the generation of
mechanical capacities. As the relationship between these
macroscopic variables encompasses the entire capability of
the neuromuscular system, it is inclusive of mechanical
properties of individual muscles (e.g. rate of force devel-
opment, and internal Fv and length-tension relationships),
morphological features (e.g. muscle architecture and ten-
don characteristics), neural mechanisms underpinning
motor-unit drive (e.g. motor unit recruitment, synchro-
nization, firing frequency, and coordination between mus-
cles), and segmental dynamics [13,18,31–33]. The Fv
mechanical profile during explosive lower limb movements
can be described by the ratio between F0and v0, or the
slope of the linear regression fit for the Fv relationship
(SFv) when force is displayed on the x-axis [28]. Additional
variables of interest are the combination of force and
velocity that elicit Pmax, often classified in literature as the
‘optimal’ level for maximal power (Fopt and vopt , respec-
tively) [34]. These variables are of particular interest to
practitioners as training implemented under a loading
scheme representative of Fopt and vopt (i.e. Lopt ) may
acutely and longitudinally improve the capacity of the
system for maximal power production [35].
2 Mechanical Profiling in Sprint Cycling
2.1 Multiple-Trial Mechanical Profiling with Cyclic
Cranks
To our knowledge, assessments of the Fv relationship using
cycling ergometry began as early as 1928 with the exper-
iments of Dickinson [36]. In this study, a mixed sex cohort
of four subjects displayed a linear relationship between
pedal rate and braking force, across increasing resistive
loads on a friction-braked cycle ergometer. The researchers
used a combination of spring balances to determine the
application of braking to the rim of the wheel, calculated as
a component of weight added to the device [37]. Despite
the fact that the results obtained by Dickinson [36] are
comparable to recent results [38], the focus of the article
and subsequent release of the hyperbolic equation by Hill
[1] limited their impact on the field of physical assessment.
Modern attempts at profiling mechanical sprinting
abilities originated based on a profiling method using a
form of Monark cyclic cranks redesigned for use with the
upper body [39] (for extensive information regarding
cyclic ergometers, see the recent detailed reviews of
Vandewalle and Driss [37] and Driss and Vandewalle [38].
The assessment protocol comprised of eight to ten sprints
performed against progressively increasing braking forces
(F;?1 kg per trial) with consideration of a curvi-linear Pv
relationship [40]. At each load, peak velocity (vmax ) was
measured and plotted against the braking load applied (see
Fig. 1). Given that at vmax the force developed by the limbs
is equal to the braking force (assuming zero acceleration),
Mechanical Profiling in Sprinting
123

the linear Fv relationship can be plotted under a least-
squares regression (see Table 1; Eq. 2) accounting for
braking force and vmax alone [40]. v0and F0were deter-
mined by the intercepts of the velocity and force axis
respectively, with Pmax referring to the optimal combina-
tion between velocity ð0:5v0Þand a load (0:5F0; Eq. 3).
These methods were later used to characterize lower body
kinetics with the development of a new ergometer (Model:
864, Monark-Crescent AB, Varberg, Sweden) featuring
higher load tolerances [30,41], and a reduced volume of
trials than these early studies (five to seven trials) due to the
Fv relationship’s linearity. Similarly, Pmax of the lower
limbs was determined as 0:25v0F0. The first methods to
profile Fv characteristics on cycle ergometry only
accounted for the force required to overcome resistive
force against the flywheel inertia (i.e. F), and not that
required to accelerate it. During the mid–late 1980s
researchers [42–44] proposed a ‘corrected’ approach that
considered the force required to accelerate the flywheel
(Facc) in addition to F, to determine a corrected force
(Fcorr) (Eq. 4). Power-output per crank revolution (Prev)
was calculated as the combination of velocity per revolu-
tion (vrev) and Fcorr , with its maximum value during
acceleration described in corrected peak-power (PPcorr ).
However, caution should be exercised when interpreting
the results of Lakomy [43] because of a small and mixed
group of participants (five males and five females) and
changes in sampling intervals [45].
2.2 Single-Trial Profiling Method with Cycle
Ergometers
Researchers realized that that once acceleration of the
flywheel was accounted for, and with technology featuring
a high enough sample rate, it was possible to plot instan-
taneous decreasing force production (inertial and friction
force) with increasing velocity during a single maximal
acceleration bout [46]. Following calculation of flywheel
inertia (see the corrected method in Sect. 2.1), the rela-
tionship between instantaneous angular crank velocity and
the torque exerted on the crank (T) were measured during a
single maximal cycle sprint (Eqs. 6–8). Variables were
assessed via a photoelectric cell measuring impulse bursts
from the flywheel up to vmax, with Tcalculated as the
combination of torque required for acceleration and torque
to overcome the braking load (see Fig. 2)[43,44].
Importantly, the torque-velocity relationship determined
via this single trial method was similarly linear, as com-
pared to the multiple-trial method. When comparing the
multiple-trial method to the newly developed single trial
method, there was no statistical difference between peak
power metrics [i.e. Pcorr vs. Pmax2 (determined as
0:25x0T0)]. Both variables were expectedly *10% higher
than the uncorrected Pmax determined from multiple trials,
which is likely a product of fatigue, reminiscent of accel-
erating to a later vmax [38,47]. The usefulness of power
correction was corroborated by Morin and Belli [48], who
Fig. 1 Graphic representation of the relationship between force-
velocity and power-velocity as profiled using a multiple-sprint
method on a treadmill ergometer. Note that graphically the same
relationship can be determined from cycle ergometry, but with torque
(Nm) against velocity (rads
-1
). Each data point represents values
derived from a single point during an individual trial at different
loading or braking protocols. F0and v0represent the yand x
intercepts of the linear regression, and the theoretical maximum of
force and velocity able to be produced in the absence of their
opposing unit. Pmax represents the maximum power produced,
determined as the peak of the polynomial fit between power and
velocity
Fig. 2 Graphic representation of force- and torque-velocity relation-
ships determined from a single trial. Torque-velocity determined via a
single-sprint method on a cycle ergometer. The method displayed
describes linear regression determined from the peak of each cycle
rotation, from the first down-stroke (First), to the last (Last). T0and v0
represent the theoretical maximum of torque and velocity, determined
via the yan xintercepts of the linear torque-velocity regression,
respectively
M. R. Cross et al.
123

reported underestimation of *20.4% for power without
accounting for the effect of inertia; however, it should be
noted that when computed from the Fv relationship, the
errors are likely lower.
As methods progressed, variables were averaged over
each pedal down-stroke [19,49,50] rather than over non-
descript periods of time. This was a biomechanically sound
progression, given that the data now represented what the
lower limbs could develop over one extension – similar to a
squat, leg press, sprinting on dynamometric treadmill or
force plate system in the ground. It should be noted,
however, that power output during cycling does not only
correspond to the pedal down stroke (when feet are strap-
ped into the pedals), but instead is produced throughout
each cycle with athletes pulling up against the pedal in
combination with pushing down [51,52]. Developments in
data collection technology allowed for more exacting
assessments of torque during cycle sprinting. For example,
Buttelli et al. [53] were the first to measure the torque
exerted over each pedal revolution during an all-out sprint
instead of computing the torque from the acceleration of
the flywheel by using a form of strain gauges bonded to the
cranks of an electric ergometer. Buttelli et al. [53] further
demonstrated that peak torque occurred later in the crank
cycle when pedalling rate increased, which was confirmed
later by Samozino et al. [19]. Furthermore, research has
implemented similar analyses of power and effectiveness
of force application, defined as the magnitude of effective
force perpendicular to the crank expressed as a percentage
of total force production [54]. This perpendicular oriented
force vector is alone necessary to rotate the drive, and
consequently has been related to mechanical efficiency
[55] and positive pedalling technique [52]. Notably, Dorel
et al. [52] clearly showed that Fv relationships are largely
affected by the mechanical effectiveness of the force pro-
duction onto the pedals, and the decrease in power output
beyond the optimal pedalling rate can be partly explained
by an important decrease in pedal effectiveness. These
analyses are of note, and their impact will be discussed
further with reference to its calculation and importance
during sprint running.
3 Mechanical Profiling During Treadmill Sprint
Running
3.1 The Beginnings of Mechanical Profiling
of Sprint Running
In order to increase assessment specificity, researchers
have endeavoured to assess mechanical capabilities during
sprint running. To our knowledge, Furusawa et al. [56]
performed the first published experiments to quantify
acceleration of track and field sprinters using a system of
wire coils, set at regular known intervals along a testing
track, connected to a galvanometer [57]. The subject was
equipped with a magnetized harness that recorded a
deflection as each coil was passed during the sprint. As the
distance (d) between each coil was known (1–10 yards),
velocity was simply calculated as v¼Dd=Dt, and accel-
eration as a¼Dv=Dt, with time measured between each
ping from the galvanometer (with a resolution of 5 ms).
The first available experimental data concerning Fv rela-
tionships during bipedal load-bearing sprinting were
derived from an experiment by Best and Partridge [8],
based on the earlier work by Furusawa et al. [56]. This
study used the same equipment with the addition of a
spectrograph split to increase the accuracy of deflection
measurement, and a customized tethered winch system to
provide a constant external resistance to the athlete. The
experiment effectively confirmed theories of the effects of
internal resistance and viscosity of muscle impeding
velocity production, and that these could be compared to
the inhibiting effects of the external resistance provided in
their study. Moreover, the study also noted the similarity of
the results to work on air resistance [56], highlighting that
the equations for estimating velocity decrement were
accurate, with the exception of the application point of
resistance (i.e. around the waist, in comparison to the
whole body). The study has subsequently been replicated
using updated technology in recent years [58].
Modern attempts at experimentally determining
mechanical characteristics of the body during load-bearing
sprinting commonly use specialized sprint treadmill
ergometry. This method requires subjects to propel a
treadmill belt while tethered around the waist to an
immovable stationary point at the rear of the machine.
These ergometers are either motorized [48,59–62], with
the motor set to apply a resistant torque to compensate for
the friction of the treadmill track under the bodyweight of
the subject, or non-motorized [63–68], with the track
simply mounted on low-friction rollers.
3.2 Multiple-Trial Methods Using Treadmill
Ergometry
To our knowledge, the first author to publish direct mea-
surements of sprint running kinetics was Lakomy [67], who
used a combination of two tests previously proposed by
Dal Monte and Leonardi [69] and Cheetham et al. [65]. Of
note, the experiments presented by Dal Monte and Leo-
nardi [69] featured the assessment of kinetics during load-
bearing running, albeit without restricted arm movement
due to the need to push against a bar to drive the treadmill
belt. Consequently, Lakomy [67] used an early non-mo-
torized treadmill (Woodway model AB, Germany) to show
Mechanical Profiling in Sprinting
123

that power, horizontal force (Fh) and velocity (vh) could be
accurately measured during a 7-s maximal sprint. While
the authors did not attempt to profile Fv relationships from
the dataset, they did confirm collection of these variables
was possible, and therefore paved the way for future
investigation. Jasko
´lska et al. [61,70] showed that a mul-
tiple-trial method could be used to accurately profile PFv
relationships on a sprint-specialized motorized treadmill
ergometer (Model: Gymroll 1800, Gymroll, Roche la
Molie
`re, France) (see Fig. 1for an example of the multiple
sprint method). To provide resistance for each loading
condition the track motors were set to apply braking, as a
percentage of a predetermined maximum value (i.e.
*1351 N) [61,70,71], to backward movement of the
treadmill belt. Resistance was increased across six sprints
(68, 108, 135, 176, 203 and 270 N), during which Fhwas
estimated via a tether-mounted force-transducer and
goniometer (to correct for attachment angle, and separate
vertically oriented forces), and vhvia a sensor system
attached to the rear drum of the treadmill belt. Instanta-
neous power was calculated as the combination of hori-
zontal force and belt velocity. These studies showed that
not only were these measurement methods sensitive
enough to determine differences between athletes of simi-
lar abilities, but the linear profile developed for each sub-
ject was independent of vmax itself. Moreover, using
various methods of variable sampling (instantaneous peak,
greatest peak value assessed from 1-s averages, total mean
and mean across 5 s), maximal power measures were
shown to be reliable [intraclass correlation coefficient
(ICC) =0.80–0.89]. When comparing PFv relationships
calculated from multiple sprints on cycle and treadmill
ergometry, Jasko
´lska et al. [70] showed power indices were
similar (r=0.71–0.86; P\0.01), albeit with lower
readings on the treadmill attributed to the load-bearing
nature of treadmill sprinting reducing maximal power
output of the lower limbs. Furthermore, the study showed
that athletes with a range of maximal speed abilities pre-
sented a linear Fv relationship when using the multiple-trial
method, with high scores for individual correlation coef-
ficients (R
2
[0.989) and no significant difference with
repeated measurement.
Since these original studies, modernized ‘two-dimen-
sional’ sprint treadmills have been shown to provide reli-
able and accurate assessment of sprinting kinetics in
various population groups [64,72–76], although none have
repeated the multiple trial PFv experiments of Jasko
´lska
et al. [61]. There are, however, limitations inherent to
treadmill-based sprinting assessment [67]. Earlier studies
[48,61,63,67,77,78] sampled instantaneous power val-
ues over non-descript brackets of time, often exceeding 1 s
in duration, resulting in the inaccurate measurement of
power and underestimation of velocity (among other
errors) [44,67]. While this limitation was often imposed by
technology, force values should be averaged over distinct
time periods relating to muscular events in the interest of
gaining a holistic view of power production specific to
step-cycles during sprint acceleration [79]. Although this
error has typically been avoided in recent studies, with high
sampling frequencies allowing averaging across definite
time-windows, this needs to be considered when inter-
preting findings from earlier studies featuring this limita-
tion. Arguably the most prominent limitation of treadmill
sprints using force transducers is that the collection of
horizontal force is an approximation, and is vulnerable to
being affected by vertical ground reaction force (FVor
GRF-z) signals as the tether moves up and down with each
step (movement of \4°;*7% contribution of vertical
force to horizontal readings) [62,67]. While some studies
have used goniometers in attempt to account for this
occurrence [59,61,70], this is not common practice
[74–76]. Moreover, although the output of power from this
method is a propulsive measure of horizontally directed
force and velocity, collection of these variables occurs in
disparate locations (along the tether and from the track
under the subject’s feet, respectively). Consequently,
kinetic output does not register a null reading between foot-
strikes (flight phase), but drops to approximately *20% of
the peak value [67], depending on technique. This is
thought to be due either to body inertia acting on the tether
during flight, some elasticity in the system, or a combina-
tion of these factors. Furthermore, significantly lower vmax
(e.g. 2.87 ms
-1
;[67]) and acceleration on these ergome-
ters are observed when they are compared to over-ground
data from the same subjects [76]. These lower values are
explained by the friction characteristics of the belt and
inertia of rolling components, and a constant manufacturer
pre-set track torque in the case of non-motorized variants,
limiting velocity-ability. This is an issue that persists even
with modernized instrumented treadmills, with the excep-
tion of feedback controlled models [80], and will be dis-
cussed in the following section.
3.3 Modern Instrumented Treadmills and the Single
Treadmill-Sprint Method
Instrumented treadmills featuring the ability to obtain
three-dimensional GRF data have been validated during
walking, running and maximal sprinting [62,78,81]. These
rare and costly machines allow collection of antero-poste-
rior, medio-lateral and vertical GRF data (in association
with velocity at foot-strike) from piezo-electric force sen-
sors positioned under the treadmill (Model: KI 9007b;
Kistler, Winterthur, Switzerland). Given the rarity and
recent development of such ergometers, until very recently
few studies have been published using such devices
M. R. Cross et al.
123

[62,82–88]. Because GRF is averaged for each single foot
contact (approximately 0.15–0.25 s) corresponding to a
single ballistic event of one push [79,89] at a high sam-
pling rate (1000 Hz) [67,79], and horizontal net power
output is calculated instantaneously as the product of hor-
izontal force and velocity (Ph¼FhvhÞcollected at the
same location (i.e. treadmill belt) (see Fig. 3), these
machines meet many of the concerns raised by previous
authors.
It was with this new instrumented sprint-treadmill
technology (Model: ADAL3D-WR; Medical Development,
HEF Tecmachine, Andre
´zieux-Bouthe
´on, France) that
Morin et al. [62] showed the ability to determine sprint
mechanics during a single sprint. In this method, Fhand vh
are averaged and plotted throughout the course of a sprint
for each stance phase similarly to each downward stroke on
pedals in early sprint-cycling studies. The steps from
maximal Fh(Fhmax ) through to that producing vhmax are
subsequently used to plot the linear Fv relationship [90].
The entire Fv relationship is described by the maximal
theoretical horizontal force that the lower limbs could
produce over one contact at a null velocity (Fh0displayed
in Nkg
-1
), and the theoretical maximum running velocity
that could be reached in the absence of mechanical con-
straints (vh0displayed in ms
-1
). A higher vh0value rep-
resents a greater ability to develop horizontal force at high
velocities. Values of horizontal maximum power (Phmax )
obtained via this method and mechanical variables (Fh0and
vh0) are congruent with results from comparable subject
pools and loading parameters in earlier studies (when
converted to similar time-periods) [48,65,66,70], and are
highly reliable for test-retest measurement (r=0.94;
P\0.01; ICC [0.90).
Similar to cycling literature [52,54], where indexes of
force application can be computed for each pedal down-
stroke, GRF output from modern treadmills can be
expressed as a ratio of ‘effective’ horizontal portion of
GRF data to the total resultant force averaged across each
contact phase (i.e. ‘ratio of forces’; RF ¼Fh=Ftot ) (see
Morin et al. [83]). Where it is possible (and encouraged) to
perform with a technique utilizing maximal RF (i.e. 100%)
in cycling, the requirement of a vertical component in
sprint running means that it is impossible to present a
maximal RF value without falling. Instead, when measured
on a sprint treadmill (from a crouched start) sub-maximal
values of RF are observed at the beginning of the sprint
(28.9–42.4%), which decrease linearly with increasing
velocity (R
2
\0.707–0.975; P\0.05) [83]. The linear
decrease in RF with velocity is described as an index of
force application technique (‘decrement in ratio of for-
ces’ =DRF), and has been shown to be highly correlated
with maximal speed, mean speed, and distance at 4 s in
100-m over-ground sprinting performance
(r=0.735–0.779; P\0.01) [83]. Practically, these vari-
ables demonstrate the ability to maintain effective orien-
tation of global force production throughout a sprint
(independently from the magnitude of the resultant GRF
output), and provide additional detailed analysis during
sprint running acceleration.
An issue that persists even with the most updated instru-
mented treadmills is the compensatory friction of the belt
appears to restrict the subject’s ability to obtain vhmax levels
near to over-ground sprint running [62,91], as previously
observed by Lakomy [67]. Furthermore, determining indi-
vidualized torque parameters is time-consuming, and
familiarization persists as a limitation with even the most
modern machines ([10 trials) [62]. Although the reduction
in sprinting velocity with torque-compensated treadmills
varies in significance between studies when compared to
over-ground sprinting (e.g. *20% of vmax ;P\0.001) [91],
one could argue the ability to measure direct kinetics over a
virtually unlimited time-period (e.g. change in mechanics
with fatigue, across 100- to 400-m distances) [92,93]
potentially outweighs these limitations.
4 Mechanical Profiling in Over-Ground Sprint
Running
Until recently, the assessment of sprint running kinetics
was only possible via the specialized treadmill ergometers
discussed in Sect. 3. While these methods have been
Fig. 3 Graphic representation of force-velocity relationship deter-
mined from a single sprint on treadmill ergometry. The data points
represent values averaged across each foot-strike, from the first (First)
to the last (Last) at peak velocity. Similar to Fig. 3,F0and v0
represent the yand xintercepts, and the theoretical maximum of force
and velocity able to be produced in absence of their opposing unit
Mechanical Profiling in Sprinting
123

markedly improved since their conception [62], the tech-
nology remains rare, assessment is costly and it requires
athletes to travel to a clinical setting. While a ‘specific’
mode of assessment, treadmill sprinting remains a dis-
similar modality of assessment compared to over-ground
sprint running performance [76,91], prompting authors to
investigate the possibility of profiling such measures during
over-ground sprinting.
Over-ground mechanical sprint profiling is somewhat
difficult due to its non-stationary nature, unlike ergometer-
based assessment, with requirements for such an approach
being the collection of high-frequency data over an accel-
eration phase until vhmax (*20–40 m in team-sport athletes,
*50–70 m in pure-speed athletes) [94]. Despite this, liter-
ature has seen kinetics directly quantified during over-
ground sprinting, either as steps within an entire sprint bout
[95–101] or instrumented load cell technology used to
determine resistive force against a weighted chariot [102]or
pulley systems [58]. Unlike the techniques developed on
cycle and treadmill ergometry, researchers have typically
ignored multiple trial methods and instead placed emphasis
on the development of PFv relationships for an unloaded (i.e.
free-resisted) sprint [90,103]. To the best of our knowledge,
there is only a single instance of researchers attempting to use
a multiple trial method overground [58], with the resultant
study methodologically unclear owing to somewhat convo-
luted design and being available only in Italian. While there
are works currently being developed (article under review)
using a full length (*50-m) force plate system to fully
measure sprinting kinetics throughout a single sprint, the
current research uses either multiple unresisted sprint
attempts over force platforms transposed together for a sin-
gle linear Fv relationship [90,103,104], or a simple method
of determining sprinting kinetics from a single sprint [90].
4.1 Composite Trial Force Plate Method
Several ground-breaking studies [105] were recently pub-
lished using a method of constructing a single composite
mechanical profile from multiple sprints performed over a
force platform system [90,103,104]. This approach, first
proposed by Cavagna et al. [106], generates an entire
mechanical Fv relationship from seven maximal sprints
performed at different starting distances behind a 6.6-m
force-plate system of six force platforms connected in series
[103]. The athletes [elite (N=4) and sub-elite (N=5)
sprinters] performed 10- to 40-m sprints, which enabled the
collection of a total of 18 foot-contacts (including those from
blocks), at 3–5 contacts per trial for greater or lesser dis-
tances, respectively. Forward acceleration of centre of mass
(COM) was calculated from contact-averaged force data,
and then expressed over time to determine instantaneous
velocity. Data were compiled to determine Fv and Pv
relationships, both of which were well described by linear
(mean R
2
[0.892) and second-order polynomial regres-
sions (mean R
2
[0.732), respectively (similarly to those
shown on earlier cycle and treadmill studies). Furthermore,
mechanical effectiveness variables were determined for each
contact phase, and correlated with overall 40-m perfor-
mances. Notably, RF averaged across the sprint performance
was shown to be the second largest differentiating factor
between elite and sub-elite sprinters [9.7%; effect size
(ES) =2.31] and the greatest correlation with overall 40-m
performance (r[0.933; P\0.01). Peak values were much
higher than those reported by Morin et al. [83]onan
instrumented treadmill (theoretical maximum
RF =70.6 ±5.4%), likely a result of the athlete starting
from sprint blocks as opposed to from a standing crouched
start. Although basic mechanical variables were shown to be
related to performance in varying degrees (e.g. v0;
r=0.803; P\0.01, and Pmax;r=0.932; P\0.001),
these results further illustrate the value in further analysis of
force orientation characteristics underpinning the horizontal
Fv relationship in sprint profiling. Overall, while the model
showed that there were no perceivable differences between
sprints for the effort involved by the sprinters
(ICC =0.686–0.958; CV =1.84–3.76%, for a range of
variables), suggesting the effects of fatigue were likely
negligible for similar highly trained sprint athletes, the
repeated nature and complexity of reproducing such mea-
sures limit its applicability in an applied setting.
4.2 Macroscopic Approach to Mechanical Profiling
during Over-Ground Sprinting
In conjunction with the methods developed by Rabita et al.
[103], Samozino et al. [90] developed a method for profiling
the mechanical capabilities of the neuromuscular system
using a macroscopic inverse dynamics approach [107],
applied to the movement of COM during a single sprinting
acceleration. This approach was similar to those proposed by
Furusawa et al. [56] and Vandewalle and Gajer [108].
Models including energetics and biomechanics have been
proposed by van Ingen Schenau et al. [109], Arsac and
Locatelli [110] and di Prampero et al. [111]. Based on the
measurement of simple velocity-time data, gathered either
by a set of photo-voltaic cells (as in the case with the primary
analysis of Samozino et al. [90]), high sample rate sports-
radar devices [90,112–114] or sports lasers [115], the
method represents a simple alternative to many of the tech-
niques discussed in this review. Such an approach makes
several assumptions: (1) the entire body is represented in
displacement of COM; (2) when averaged across the accel-
eration phase, no vertical acceleration occurs throughout a
sprint (see limitations of the treadmill sprint method in
Sect. 3[67]); and (3) the coefficient of air drag remains
M. R. Cross et al.
123

constant (e.g. changes in wind strength). While not an
inherent limitation due to its ease of implementation, vari-
ables are modelled over time without consideration of
changes between and within steps, inclusive of both support
and flight phases, rendering assessment and comparison of
individual limb kinetics impossible.
In this method, a mono-exponential function
[56,108,110,116,117] is applied to the raw velocity-time data
(Table 2; Eq. 9). After this, the fundamental principles of
dynamics in the horizontal direction enable the net horizontal
antero-posterior GRF to be modelled for the COM over time,
considering the mass (m) of the athlete performing the sprint in
association with the acceleration of COM, and the constant
aerodynamic friction of the body in motion (Faero)(Eqs.10,
11). Fhand vhvalues are then plotted to determine Fv rela-
tionships and mechanical variables (Fh0and vh0). As with
previous methods, Phmax can be calculated as the interaction
between Fh0and vh0(Eq. 5) [28,90,118], and by the peak of the
second-order polynomial fit between Phand vh.Furthermore,
technical variables (RF and DRF ) can be calculated similarly to
previous methods [83,90,103], with the resultant force (Fres)in
this case being computed from estimated net vertically (see
Eq. 12) and horizontally oriented GRFs. Where previous
studies calculated technical variables from the second step, in
this case the variables are instead calculated from 0.3 s, given
determining individual step characteristics is impossible.
Importantly, Samozino et al. [90] highlighted that the
macroscopic inverse dynamic approach was very similar to
the multiple force plate method for GRF modelled and com-
putedovereachstep(Fh,Fres, vertical force (i.e. Fv);
r=0.826–0.978; P\0.001). Furthermore, low absolute
bias was observed between methods for physical
(1.88–8.04%) and technical variables (6.04–7.93%). Data
were extremely well fitted with linear and polynomial
regressions (mean R
2
=0.997–0.999), with all variables
presented as reliable (CV and standardised error of measure-
ment\5%) [90]. These results serve to illustrate the strength
of such an approach—that estimation of over-ground sprint-
ing kineticsvia this simple field method is practically identical
to direct measurement via a complex force-plate setup. Fur-
thermore, the method has been shown to be sensitive enough
to highlight differences in mechanical variables between
athletes with similar abilities, determine between playing
positions and track return from injury of rugby and soccer
athletes in the field [112–114]. Given the only data required is
velocity-time measured with sufficient sampling rate, any
practitioner with a reasonable set of photovoltaic timing gates
(i.e.[4 sections), sports radar or even simple cellular devices
(MySprint application) [119] could potentially use such a
profiling method during their training and assessment batteries
[120]. While it is technically possible to apply the same
method to the data gained from widely available global
positioning systems [121], the specifications of current com-
mercial units limit the accuracy of such technology for
meaningful performance inferences.
While limited in its ability to quantify individual limb
kinetics, the simplicity and ease of implementation of this
method suggests value for practitioners who might other-
wise be unable to access the technology required to accu-
rately assess sprinting mechanics.
5 Optimal Loading, Training Considerations
and Future Research
Mechanical profiling allows the computation of the exact
conditions underlying maximal power to be determined.
These parameters, regularly termed ‘optimal’, represent a
Table 2 Development of computational methods for over-ground sprint running
Study and mechanical profiling type Formula Equation number
Furusawa et al. [56]
Exponential function of COM velocity-time relationship
in sprinting
vhðtÞ¼vhmax :ð1et=sÞ[9]
Samozino et al. [90]
Acceleration and horizontal orientation of COM travel
conveyed as a derivation of velocity over time
xhtðÞ¼
r
vhðtÞdt¼
r
vhmax 1et=sðÞ

dt
xhtðÞ¼vhmax tþs:et=s

vhmax s
ahtðÞ¼dvhtðÞ
dt¼vhmax 1et=s
ðÞ
dt¼vhmax
s

et
s
ðÞ
[10]
Arsac and Locatelli [110]
External horizontal net force modelled over time with
consideration for air friction
FhtðÞ¼mahtðÞþFaero tðÞ [11]
di Prampero et al. [111]
Net vertical ground reaction force modelled over time FVtðÞ¼mg[12]
COM centre of mass, vhhorizontal force, vhmax maximum horizontal force obtained during over-ground locomotion, sacceleration time constant
in seconds, xhhorizontal orientation of centre of mass, ddistance, ttime, aacceleration of centre of mass, m body-mass, Faero aerodynamic
friction force, FVnet vertical force occurring, ggravitational acceleration (-9.81 ms
-2
)
Mechanical Profiling in Sprinting
123

combination of force and velocity values (i.e. Fopt and vopt ),
at which a peak metric of power is maximized (see Fig. 3)
[34]. Of note, training in these conditions has been sug-
gested as an effective method of increasing the capacity for
power production [21,35], which may improve practical
performance measures provided the subject displays a
favourable profile of Fv capacities [24]. Practically, in
order for these data to prove valuable, they require trans-
lation into an easy-to-set normal load (Lopt), either as
bandwidth or individual value of external stimulus, that
stimulates the mechanical conditions necessary to maxi-
mize power production during training.
5.1 Optimal Loading in the Literature
Typically, the literature has shown that PFv and optimal
loading characteristics are specific to movement type
[28,35,122,123], with a recent meta-analysis [21]
describing bandwidths of 0–30% of one-repetition-maxi-
mum (1RM) for jump squat movements, 30–70% 1RM for
squat movements, and [70% of 1RM for the power clean
movement. While increases in mechanical capacity are
likely dependent on a number of factors, the literature
supports the value of training at levels around optimal
(Lopt,Fopt , and vopt )[124] in a movement transferrable to
performance. Furthermore, in limited examples the appli-
cation of optimal force can directly influence performance
in competition scenarios [52]. Specifically, optimal loading
conditions as assessed in sprint cycling [125], in near
competition-specific conditions, can be replicated by
manipulating crank length and gear ratios to enable the
athlete to perform a cycle race in practically optimal con-
ditions for power production [126]. There is evidence to
suggest performing and training closer to Fopt may be
beneficial for a host of acute performance properties in
cycling, including increased mechanical effectiveness
[127,128], decreased movement energy cost
[127,129,130], reduced negative muscle actions [131],
increased metabolic ratio [127,132] and increased resis-
tance to fatigue [133,134]. These factors strengthen the
rationale for profiling these characteristics where the
mechanical constraints during competition can be altered to
replicate optimal levels.
Unfortunately, reviews of optimal loading [21,35] have
largely focused on acyclic ‘single extension’ movements
using free-weights or smith machines. Furthermore, research
examining these themes in cyclic movements has almost
exclusively focused on cycling, with differing methods,
equipment, varying athlete training backgrounds and per-
formance levels rendering comparison between studies dif-
ficult [135,136]. Of the few studies that examine optimal
loading for sprint running on treadmill ergometers, Jasko
´lski
et al. [71] showed that athletes produced peak power at a
variable resistance (i.e. torque applied to the belt) of 137–
195 N (10.1–14.5% of maximal inbuilt braking resistance)
for a range of power indices, and proposed that the results
may be dependent on athlete strength and anthropometric
characteristics. A few years later, Jasko
´lska et al. [70]
reported similar results in a group of students [N=32;
optimal loading =176–203 N (13–15% braking force)].
However, both studies simply reported the protocol that
presented the greatest level of power, rather than fitting the
data with regression equations (i.e. second- or third-order
polynomial), to determine the exact point on the Fv/Lv
relationship at which power was maximized [49,137,138].
In the latter example, the authors acknowledge that 34% of
the athletes did not reach a measurable peak or decline in
their power-capabilities with the heaviest loading protocol,
and consequently the results likely understated the
mechanical capacity of the cohort. A more recent study by
Andre et al. [139], suffering from the same limitations, found
that most athletes in their sample (*73%) produced their
peak power between 25 and 35% of body mass (BM), based
on the unsubstantiated manufacturer pre-set electromagnetic
braking resistance for treadmill ergometer (Model: Wood-
way Force 3.0, Eugene, OR, USA). In contrast, using a
modern instrumented treadmill, Morin et al. [62] showed
three increasing levels of braking resistance did not signifi-
cantly alter Pmax determined during a single sprint, remi-
niscent of increased force and decreased velocity output.
This was mainly due to the fact that (1) power output was
measured continuously during the sprint acceleration (in
contrast to vmax plateau in previous multiple trials method)
and (2) maximal power was reached during the acceleration
phase (but not at the same time) whatever the braking
resistance. In any case, while the determination of optimal
loading on treadmill ergometry offers an additional value by
which to measure athlete ability, its relation to training
implementation is limited to the assessment modality itself.
That is, the conditions determined in these studies may only
be replicated in training with access to specialized treadmill
ergometry.
5.2 Optimal Conditions for Loading in Over-
Ground Sprinting
At this stage, to the best of our knowledge no literature has
clearly reported the methods necessary to profile practical
optimal loading conditions during over-ground sprinting.
That is, no research has used a multiple trial method with
progressive resistance, such as sprinting sleds, braking
devices or cable winches, to profile PFv relationships that
can be understood and replicated with scientific rigor.
While optimal loading conditions for sprint running
M. R. Cross et al.
123

training modalities over ground have been discussed
[120,124,135,140], authors have typically limited loading
to that which maximizes external stimulus without signif-
icantly altering kinematics of the unloaded sprint move-
ment (e.g. \10% decrease in vmax,or\12.6% of BM)
[140–142]. While training in this manner no doubt achieves
the goal of maintaining absolute kinematic similarity to
unresisted performance, there is evidence to suggest that
these loading protocols are far from the conditions neces-
sary for development of maximal power. Of note, the fact
that Fopt and vopt occur at approximately half of the max-
imum velocity attained in an unloaded sprint (0:5F0and
0:5v0,[34]) would appear to challenge these guidelines,
provided increased Pmax is the goal. Recent evidence sug-
gests training at heavier loads versus more traditional,
lighter loading protocols benefits sprint running perfor-
mance to a greater degree (i.e. 10 vs. 43% of BM loading
onto a resistive sled device) [35,95]. To date, while vopt
has been reported in elite rugby athletes at between 4.31
and 4.61 ms
-1
[113], no specific optimal loading/training
strategy has been determined for over-ground sprinting
regarding power development. The effects of sprint train-
ing using loading protocols of such magnitude (e.g. 50%
velocity decrement), both acute and longitudinal perfor-
mance outcomes, are yet to be quantified.
5.3 Implications for Training, and Future Research
The relationship between Fv properties, as illustrated by
the slope of the linear regression fit (SFv), denotes that Pmax
and SFv are independent from one another. Evidence sug-
gests performance in both jumping and sprint running is
reliant not only on the expression of Pmax, but also on the
absolute level and balance between Fv components
[28,83]. Practically, two athletes exhibiting identical Pmax
values could present markedly different Fv relationships
(as a function of either a higher or a lower F0or v0)
[28,83], which may be evident in practical performance
measures [120]. Considering Fv characteristics in single
extension movements have recently been determined as
individualized [24,28], it would seem exercise and load
prescription should occur based on both SFv and Pmax
qualities [120]. While training at Lopt may be a simple
approach to increase Pmax , targeted programming may see
prescription of greater or lesser load (force or velocity
dominant stimuli, respectively) depending on the orienta-
tion of SFv and the targeted task (e.g. sprint distance to
optimize, or level of resistive force to overcome). Impor-
tantly, this is an integrative multi-factorial approach, and
targeted training based on SFvorientation may not be as
important to novice athletes, who will likely see increases
in performance with basic prescription, as opposed to
highly-trained athletes. Furthermore, there is currently little
research investigating these theories in practice, none of
which exists in the realm of sprint running; hence inves-
tigation of this nature is required.
6 Conclusions
The Fv relationship and maximal power capacity offer
understanding of the limits of the human body for sprinting
performance. These mechanical capabilities can be accu-
rately measured by various methods during acceleration
sprinting in cycling and sprint running (treadmill and
overground). While it is well known that adaptations are
specific to the velocity used in training, there is an overall
paucity of research using PFv methods on updated equip-
ment, and further investigation is required in longitudinal
studies. Given the rapid development of easily accessible
profiling methods, research providing normative data on
athletes from varying performance levels using modern
technologies would provide insight into the mechanical
performance requirements of unique sporting cohorts.
Elucidating these normative or optimal characteristics,
including methods through which to implement meaningful
changes, would prove invaluable in the guidance of indi-
vidualised and targeted training programs to increase the
capacities underlying maximal sprinting performance.
Compliance with Ethical Standards
Funding No funding was received for this review which may have
affected study design, data collection, analysis or interpretation of
data, writing of this manuscript, or the decision to submit for
publication.
Conflict of interest Matt R. Cross, Matt Brughelli, Pierre Samozino
and Jean-Benoit Morin declare that they have no conflicts of interest
that are directly relevant to the content of this review.
Author contributions All authors were involved in the preparation
of the entire content of this manuscript.
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