lees 2000
TRANSCRIPT
The energetics and benefit of an arm swing in submaximal and maximalvertical jump performance
ADRIAN LEES1, JOS VANRENTERGHEM2, & DIRK DE CLERCQ2
1Research Institute for Sport and Exercise Sciences, Liverpool John Moores University, Liverpool, UK and 2Department of
Movement and Sports Sciences, Ghent University, Ghent, Belgium
(Accepted 11 May 2004)
AbstractThe aims of this study were to investigate the energy build-up and dissipation mechanisms associated with using an armswing in submaximal and maximal vertical jumping and to establish the energy benefit of this arm swing. Twenty adult maleswere asked to perform a series of submaximal and maximal vertical jumps while using an arm swing. Force, motion andelectromyographic data were recorded during each performance and used to compute a range of kinematic and kineticvariables, including ankle, knee, hip, shoulder and elbow joint powers and work done. It was found that the energy benefit ofusing an arm swing appears to be closely related to the maximum kinetic energy of the arms during their downswing, andincreases as jump height increases. As jump height increases, energy in the arms is built up by a greater range of motion at theshoulder and greater effort of the shoulder and elbow muscles but, as jump height approaches maximum, these sources aresupplemented by energy supplied by the trunk due to its earlier extension in the movement. The kinetic energy developed bythe arms is used to increase their potential energy at take-off but also to store and return energy from the lower limbs and to‘‘pull’’ on the rest of the body. These latter two mechanisms become more important as jump height increases with the pullbeing the more important of the two. We conclude that an arm swing contributes to jump performance in submaximal aswell as maximal jumping but the energy generation and dissipation sources change as performance approaches maximum.
Keywords: biomechanical analysis, kinematics, kinetics
Introduction
It is well established that if the arms are swung
upwards when jumping maximally for height, jump
height improves by 10% or more compared with
when the arms are not used (Harman, Rosenstein,
Frykman, & Rosenstein, 1990; Lees, Vanrenterghem
& De Clercq, 2004; Luhtanen & Komi, 1979; Shetty
& Etnyre, 1989). This improvement in performance
comes from both increased height and velocity of the
centre of mass at take-off. The increase in centre-of-
mass height is due directly to the elevation of the
arms but it is the increase in velocity of the centre of
mass that has the greatest influence on performance.
Recent investigations have shown that increased
velocity of the centre of mass contributes between
60% (Feltner, Frasceti, & Crisp, 1999) and 72%
(Lees et al., 2004, 37, 1929 – 1940) to the increase
in performance. Our own work (Lees, as above)
has shown that this increased velocity stems from a
complex series of events that allows the arms to build
up energy early in the jump and then transfer this
energy to the rest of the body during the later stages
of the jump. The energy built up by the arms (which
accounted for some 16% of the total work done
during the jump) comes from the muscles of the
shoulders and elbow joints as well as extra work done
by the muscles around the hip joint as the hip
extends to initiate the upward movement of the
centre of mass. The energy of the arms was used (1)
to increase the kinetic and potential energy of the
arms at take-off, (2) to store and release energy from
the muscles and tendons around the ankle, knee and
hip joints, and (3) to increase the energy of the rest of
the body through the transmission of a pull force at
the shoulder joint. The resulting energy benefit of
using an arm swing was estimated to be between 0.98
and 1.21 J � kg71 (corresponding to 12 and 15%
respectively of total work done), with the upper value
being thought the more reasonable estimate.
It is clear from our previous investigation that
several mechanisms are used to create an energy
benefit when using an arm swing. What is not known
is whether these mechanisms operate in the same
Correspondence: A. Lees, Research Institute for Sport and Exercise Sciences, Liverpool John Moores University, 15 – 21 Webster Street, Liverpool L3 2ET,
UK. E-mail: [email protected]
Journal of Sports Sciences, January 2006; 24(1): 51 – 57
ISSN 0264-0414 print/ISSN 1466-447X online ª 2006 Taylor & Francis
DOI: 10.1080/02640410400023217
way when submaximal jumping is performed. The
aims of this study were to investigate the energy
build-up and dissipation mechanisms associated with
using an arm swing in submaximal and maximal
vertical jumping and to establish the energy benefit of
this arm swing.
Methods
To investigate the contribution that joints make to
the vertical jump, a progressive performance para-
digm was used. This required participants to perform
a counter-movement vertical jump at a given sub-
maximal height (termed ‘‘LOW’’), then again at a
greater height (termed ‘‘HIGH’’) and then finally for
maximal height (termed ‘‘MAX’’). The LOW and
HIGH conditions were controlled for each partici-
pant by a target mounted above the participant’s
head. The data for the MAX condition have
previously been reported in Lees, 2004, 37, 1929 –
1940. Twenty athletic adult males (mean+ s: age
19.9+ 3.9 years, height 1.80+ 0.07 m, mass
75.4+ 13.3 kg) participated in the investigation.
All of the participants were competitively active in
sports, which ranged from field games play to
gymnastics. All participants were fit and free from
injury and each provided informed consent as
required by the university’s ethics committee.
Data collection
Participants were given the opportunity to warm up
with light exercise and stretching, and to practise the
three types of jump. They were required to perform
three repetitions of each condition using a natural
jumping technique that included the use of an arm
swing. The participants performed each jump on a
force platform (Kistler, Winterthur, Switzerland).
Reflective markers were placed over the second
metatarsal-phalangeal joint, lateral malleolis, lateral
knee, hip, wrist and elbow joints, acromion process,
C7 and on the vertex of the head using a marker
placed on the top of a cap worn on the head. The
three-dimensional position of each marker was
recorded using a six-camera opto-electronic motion
capture system (Proreflex, Qualysis, Savedalen,
Sweden). Data were collected for a period of 6 s,
which allowed approximately 2 s of quiet standing
before the jump commenced. The motion data were
collected at 240 Hz, while the force data were
collected at 960 Hz. All data were electronically
synchronized in time.
Data reduction
Kinematic analysis procedures. The three-dimensional
motion data from the 16 markers were used to define
a 12-segment biomechanical model using segmental
data proposed by Dempster (1955) for adult males.
These data were used to calculate the segment and
whole-body centre-of-mass locations. As vertical
jumping is essentially a sagittal plane activity, the
data were projected onto the sagittal plane to
compute segment orientations and joint flexion
angles. All kinematic data were then smoothed using
a low-pass Butterworth fourth-order, zero-lag filter
with padded end-points (Smith, 1989) and a cut-off
frequency of 7 Hz based on a residual analysis and
qualitative evaluation of the data. Derivatives were
calculated by simple differentiation (Winter, 1990).
Kinetic analysis procedures. The force data were
averaged over four adjacent points so that each force
value corresponded to each motion data value at 240
Hz. Inverse dynamics using standard procedures
(Miller & Nelson, 1973; Winter, 1990) was used to
compute the segment proximal and distal net joint
forces and net joint torques at the ankle, knee and
hip. Joint power (the product of net joint torque and
joint angular velocity) and work done (the time
integral of the power production at a joint between
specified time points) were calculated based on
standard procedures (de Koning & van Ingen
Schenau, 1994). Extension joint torque is presented
as positive while flexion joint torque is negative.
Similarly, joint power generation is presented as
positive while joint power absorption is negative. For
all joint variables, the sum of the left and right limbs
was computed. All kinetic variables were normalized
to body mass to reduce the influence of body mass
on the values computed.
Presentation of data. Data are presented over the
period from the start of the movement to take-off.
The start and end were defined when the vertical
ground reaction force went above or below a
threshold value. This also defined the movement
time of the action, which was isolated and normal-
ized to 100 points. Finally, each normalized trace
was averaged over all participants and all trials (total
of 60 data sets per condition) to provide a mean
curve for that variable.
Statistical analysis
A one-way analysis of variance with a post-hoc
Tukey test was used for establishing differences,
and a value of P5 0.05 was used to indicate
statistical significance.
Results
Descriptive data for each jump condition are given
in Table I. As the jump condition changed from
52 A. Lees et al.
LOW through HIGH to MAX, jump height relative
to the standing position increased, with the LOW
and HIGH performances being 65% and 83% of
MAX, respectively. The greater jump height was
associated with a greater depth of counter-movement
(see also Figure 1), greater forward inclination of the
trunk during the counter-movement, and greater
height of the centre of mass at take-off. The greater
height of the centre of mass at take-off was due to the
greater elevation of the arms. These greater ranges of
movement took longer to complete and so the
movement duration increased.
The joint powers reflect both the joint torques and
joint angular velocities and for the ankle, knee and
hip (Figure 2) the greatest power was produced in
the later phase of the movement, whereas for the
shoulder and elbow it was produced during the
earlier part of the movement (Figure 3). Peak power
at the ankle remained unchanged as jump height
increased, while peak power for the knee reduced
and peak power at the hip increased.
The total work done by the body (Table II) was
computed from the total distance moved by the
centre of mass through the upward extension phase
until it reached the apex of its flight. This was larger
in the higher jumps because of the lower initial
position and the higher final position. Any horizontal
or rotational energy the body may have had was
ignored. The work done at the ankle, knee and hip
joints (Table II) was computed from the integral of
the positive power during the ascent only. The work
done by the knee increased non-significantly as jump
height increased (F2,20 = 1.492, P = 0.234), while at
the ankle it increased slightly (F2,20 = 3.596,
P = 0.034) and the hip it increased markedly
(F2,20 = 110.143, P5 0.001). The work done at
the shoulder and elbow joints was computed from
the integral of the positive power during the start of
the arm downswing to take-off. Both increased as
jump height increased and this was associated with a
greater range of motion of both joints.
The arms can be treated as an energy system
where all energy calculations are made relative to the
shoulder joint (which is considered to be a fixed
point within the biomechanical model of the body
used here). Once the position of maximal retraction
of the arms was attained, this was followed by a
downswing and upswing phase, respectively. The
total energy delivered to the arms at the end of the
downswing [TE(arms)downswing; Table III, item b]
was computed from the reduction of potential energy
of the arms system [PE(arms)downswing] during the
downswing plus the positive work done on the arms
at the shoulder ( + WDshoulder; Table III) plus half of
the positive work done by the elbow ( + WDelbow)
(half, as only this amount is done by the time the
arms reach the end of their downswing). The
difference between this and the measured linear
and rotational kinetic energy of the arms system at
the bottom of the downswing [KE(arms)downswing;
Table III, item c] is a measure of the energy fed into
the arms system due to trunk extension during the
downswing (Table III, item d). Table III shows that
as jump height increases, the arms begin the down-
swing from a more hyper-extended position enabling
them to have greater potential energy, they reach a
greater kinetic energy at the bottom of the down-
swing and more work is done on the arms by the
trunk. However, the work done by the trunk is
negligible for the LOW jump height and this suggests
that using the trunk to generate higher energy in the
Table I. Performance variables for the three jump conditions (mean+ s)
LOW HIGH MAX P
Height jumped (m) * 0.346+ 0.027 0.442+ 0.030 0.533+ 0.043 5 0.001
Deepest point (m) * 70.171+ 0.022 70.216+ 0.038 70.297+ 0.057 5 0.001
Trunk flexion angle (8) 14.4+ 7.1 25.8+ 7.2 44.8+ 9.5 5 0.001
Centre-of-mass height at
take-off (m) *
0.108+ 0.019 0.126+ 0.023 0.140+ 0.049 5 0.001
Duration of action (s) 0.729+ 0.104 0.812+ 0.126 0.962+ 0.144 5 0.001
* Relative to standing height.
Figure 1. Averaged time-normalized graphs for the vertical
position of the centre of mass for jumps in the LOW, HIGH
and MAX conditions.
Arm swing in vertical jump performance 53
arms is a characteristic only of higher performance
jumps.
As the arms make their upward swing, their
kinetic energy is dissipated in a complex series of
energy transformations. At take-off, the arms
system has regained potential energy [PE(arm-
s)take-off] and a small residual amount of kinetic
energy [KE(arms)take-off], and if this is deducted
from KE(arms)downswing and the remaining 50% of
the elbow work done is added, the residual (Table
III, item f) is a measure of the energy dissipated.
Deducting the negative work by the joint moment
at the shoulders (-WDshoulders; Table III, item g)
gives the energy available for dissipation through
the forces acting at the shoulder and this mechan-
ism is described as ‘‘pull’’ (Table III, item h). A
second estimate for pull can be made using the
integral of the product of vertical net joint force
acting at the shoulders and the velocity of the
shoulder joint when the vertical net joint force is
acting in an upward direction, which is for
approximately the last 10% of the jump (Table
III, item j).
Finally, the energy benefit of the arm swing can be
calculated as the sum of the potential energy of the
arms at take-off, the residual kinetic energy of the
arms at take-off, the energy delivered through pull
and the return of stored elastic energy. The latter
energy value cannot be calculated precisely but for a
maximal counter-movement jump Lees, 2004, 37,
1929 – 1940 have estimated the energy return as
0.35 J � kg71 for an energy input of 0.83 J � kg71,
giving an efficiency factor of 42%. If this factor is
used for all jump heights, a value for energy return
can be estimated (Table III, item k) and the total
energy benefit of the arm swing calculated using
the first (Table III, item l) and second estimates
(Table III, item m) for pull.
Discussion
A progressive performance paradigm was used to
evaluate the contribution of the arm swing to jump
height, as jump height increased to a maximum
value. In the vertical jump, the arms are progressively
used more forcefully as jump height increases,
illustrating that they have a significant role to play
in generating jump height. As jump height increases,
the arms are hyper-extended to a greater extent and
go through a greater range of motion. The greater
hyper-extension means that more potential energy is
available to increase the kinetic energy of the arms at
the lowest point of their downswing. This is
complemented by greater work done at both the
shoulder and the elbow, which also serves to increase
the kinetic energy of the arms. The discrepancy
between the energy available to the arms and their
kinetic energy at the end of the downswing is
interpreted as indicating some energy input into the
arms system from the forces acting at the shoulder.
This energy input comes from the trunk due to hip
extension and is quite large for the MAX jump
condition (approx 0.3 J � kg71) but negligible for the
LOW jump condition. This suggests that the energy
build-up mechanisms change as the demand for
height increases – in other words, as jump height
increases, there is greater emphasis placed on trunk
Figure 2. Averaged time-normalized graphs in each jump
condition for joint powers at (a) the ankle, (b) the knee and (c)
the hip.
54 A. Lees et al.
extension, which has the effect of increasing the
energy of the arms during the downswing.
Then, as the arms swing upwards their energy
reduces. Some of this energy goes into increasing
their potential energy and providing for the small
residual kinetic energy at take-off. The remainder of
the energy is dissipated and this mainly occurs
through the negative work done by the joint moment
at the shoulders and through the vertical net joint
force at the shoulder that acts upwards to ‘‘pull’’ on
the rest of the body.
Two estimates for the energy dissipated through
pull have been made, first by energy accounting
and second by using the net joint force at the
shoulder. We regard the latter estimate as our
preferred estimate, as there was some evidence
(Lees, 2004, 37, 1929 – 1940) that energy can be
transferred between the arms and the trunk during
the upswing in a similar way as in the downswing. If
this was happening, then the energy for dissipation
by ‘‘pull’’ would be different than that estimated by
energy accounting (item h in Table III) and be better
estimated by a direct calculation of this variable using
the net joint force (item j in Table III). The greater
value of the second estimate for the MAX jump
condition suggests that there is a substantial energy
inflow to the arms system in this condition, but it is
Figure 3. Averaged time-normalized graphs in each jump
condition for joint powers at (a) the shoulder and (b) the elbow.
Table II. Total work done based on the distance moved by the
centre of mass from its lowest point to its apex; work done
(mean+ s) at the ankle, knee and hip joints during ascent and at
the shoulder and elbow joints from the start of the downswing until
take-off (all units are J � kg71)
LOW HIGH MAX
Total work done 5.072 6.455 8.142
Joint work at ankle 1.80+ 0.33 1.97+ 0.28 2.06+ 0.35
Joint work at knee 1.62+ 0.63 1.77+ 0.58 1.94+ 0.47
Joint work at hip 1.03+ 0.28 1.84+ 0.47 3.24+ 0.6
Total lower joint
work
4.764 6.209 8.151
Joint work at
shoulder
0.20+ 0.17 0.41+ 0.23 0.63+ 0.27
Joint work at
elbow
0.11+ 0.08 0.22+ 0.14 0.30+ 0.20
Table III. Energy variables for the three jump conditions (all units
are J � kg71) (mean+ s)
LOW HIGH MAX
Downswing
PE(arms)downswing 0.075 0.129 0.257
+ WDshoulder 0.204 0.409 0.628
+ WDelbow * (a) 0.055 0.112 0.151
TE (arms)downswing (b) 0.334 0.650 1.036
KE (arms)downswing (c) 0.344 0.701 1.319
WD by hip on arms
(d = c – b)
0.010 0.051 0.283
Upswing
PE(arms)take-off (e1) 0.118 0.217 0.300
KE(arms)take-off (e2) 0.017 0.027 0.100
Energy available for
dissipation
(f = b – e1 – e2 + a)
0.264 0.567 1.059
7WDshoulders (g) 70.121 70.322 70.834
Work available for pull
(h = f – g)
0.143 0.245 0.225
Work done by pull ** (j) 0.087 0.282 0.458
Return of stored energy
(k = 42% of g)
0.060 0.103 0.35
Benefit of arm swing
First estimate
(l = e1 + e2 + h + k)
0.338 0.592 0.975
Second estimate
(m = e1 + e2 + j + k)
0.282 0.629 1.208
* Represents half the work done by the elbow as half is done during
the downswing and half during the upswing.
** Computed from the vertical force acting at the shoulder.
Note: + WD = positive work done; -WD = negative
Arm swing in vertical jump performance 55
neutral for the HIGH jump condition, and in the
LOW condition the arms appear to continue to loose
energy. This mechanism appears to act differentially
with regard to jump height, benefiting maximal
performance but penalizing submaximal perfor-
mance. A more detailed analysis of power flows
across the shoulder joint is required to clarify this
speculation.
The dissipation of energy associated with the
negative work done by the shoulders has been
associated with the storage of elastic energy in the
muscles and tendons of the ankle, knee and hip
(Lees, 2004, 37, 1929 – 1940), and a value for the
return of this energy for the MAX condition has been
estimated by comparing arm swing with no-arm
swing jumps. It is not possible to estimate the return
energy for the other jumps used in this study, so as a
first approximation the efficiency value of 42%
obtained for the MAX jump condition was used.
This led us to estimate that the returned energy was
negligible for the LOW condition but became
increasingly more important as the jump height
increased. However, it should be stressed that we
do not have any detailed information regarding the
efficiency of energy return in such circumstances.
Taking the estimations and approximations above,
the energy benefit of using the arms appears to
increase from 0.282 J � kg71 (6% of total work done)
in the LOW jump condition to 1.208 J � kg71 (15%
of total work done) in the MAX jump condition. If
the maximum kinetic energy in the downswing is
compared with the energy benefit, it can be seen that
there is a high efficiency for all jump heights (based
on the second estimate, item m in Table III, the
efficiency is 82%, 90% and 92% for the LOW,
HIGH and MAX jumps, respectively). The energy
benefit appears to be highly related to the maximum
energy of the arms (item b in Table III) and this may
provide a good rule of thumb for future estimations
of the energy benefit of using the free limbs to aid
jump performance when only kinematic data are
available.
The manner in which the energy built up in the
arms is used appears to change as the jump height
increases. The energy used to raise the arms in the
upswing accounts for 42%, 34% and 25% of the
energy benefit in the LOW, HIGH and MAX
conditions, respectively, with the residual used to
increase the velocity of the centre of mass. (The
estimates for the MAX condition are in close
agreement with the 28% and 72% reported in the
Introduction.) The residual can be further divided
into that associated with the pull on the body and
that associated with the return of stored elastic
energy. The percentage of energy accounted for by
pull is 31%, 45% and 38%, and for energy return
21%, 16% and 29%, in the LOW, HIGH and MAX
conditions, respectively. The trend in the data
suggests that the velocity-producing components of
the energy benefit increase as jump height increases,
which is to be expected, but the pull appears to be a
more important mechanism than the return of stored
energy. Any trend in the relative importance of each
is clouded by the values for the HIGH condition.
There are some aspects of this analysis that require
further comment. One is the discrepancy between
the work done by the joints and the total work done
in elevating the centre of mass (Table II). It is
expected that the work done by the joints exceeds the
total work done in elevating the body because some
rotational energy is present in the body segments.
Hatze (1998) has estimated that this is about 3% and
so provides a guide for the error that may exist in the
data reported here. While the agreement is good for
the MAX condition, it is less so for the LOW
condition. It is unclear why this might be the case.
One possible explanation is that energy sources exist
from joints that have not been included within this
analysis, one being due to the flexible nature of the
trunk, another being the use of shoulder elevation in
preference to shoulder rotation. It is not possible to
resolve the discrepancy with the data reported here.
A second point is the assumption that the energy
return efficiency is similar for all conditions. This is
unknown but if it were less efficient for the LOW
jumps, this would have the effect of reducing the
energy benefit of the arm swing, thus making the
potential energy and pull mechanisms relatively
more important. The converse would be true if
the efficiency were greater. However, because of the
relatively low values of return of stored energy for
the LOW jump conditions, it is not thought that
this would have a marked effect on the interpretation
of the data.
In summary, the aims of this study were to
examine the energy build-up and dissipation me-
chanisms associated with using an arm swing in
submaximal and maximal vertical jumping and to
establish the energy benefit of this arm swing. The
energy benefit of using an arm swing increases as
jump height increases. As jump height increases,
energy in the arms is built up by a greater range of
motion at the shoulder and greater effort of the
shoulder and elbow muscles; however, as jump
height approaches maximum, these sources are
supplemented by energy supplied by the trunk due
to its earlier extension in the movement. Emphasiz-
ing early trunk extension may therefore be one
method for improving the technique of jumping for
height. The energy of the arms is used to increase
their potential energy but in particular to store and
return energy from the lower limbs and to ‘‘pull’’
on the rest of the body. These latter two mechan-
isms become more important as jump height
56 A. Lees et al.
increases, with the pull being the more important of
the two.
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Arm swing in vertical jump performance 57