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: humalees@livjm.ac.uk

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.

References

de Koning, J. J., & van Ingen Schenau, G. J. (1994). On the

estimation of mechanical power in endurance sports. Sports

Science Review, 3, 34 – 54.

Dempster, W. T. (1955). Space requirements of the seated operator.

WADC Technical Report #55 – 159. Ohio: Wright-Patterson

Air Force Base.

Feltner, M. E., Frasceti, D. J., & Crisp, R. J. (1999). Upper

extremity augmentation of lower extremity kinetics during

countermovement vertical jumps. Journal of Sports Sciences, 17,

449 – 466.

Harman, E. A., Rosenstein, M. T., Frykman, P. N., & Rosenstein,

R. M. (1990). The effects of arms and countermovement on

vertical jumping. Medicine and Science in Sports and Exercise, 22,

825 – 833.

Hatze, H. (1998). Validity and reliability of methods for testing

vertical jumping performance. Journal of Applied Biomechanics,

14, 127 – 140.

Lees, A., Vanrenterghem, J., & De Clercq, D. (2004). Under-

standing how an arm swing enhances performance in the

vertical jump. Journal of Biomechanics, 37, 1929 – 1940.

Luhtanen, P., & Komi, P. V. (1979). Mechanical power and

segmental contribution to force impulses in long jump take off.

European Journal of Applied Physiology, 41, 267 – 274.

Miller D. I., & Nelson, R. C. (1973). Biomechanics of sport (pp.

39 – 88). Philadelphia, PA: Lea & Febiger.

Shetty, A. B., & Etnyre, B. R. (1989). Contribution of arm

movement to the force components of maximal vertical jump.

Journal of Orthopaedic and Sports Physical Therapy, 11, 198 –

201.

Smith, G. (1989). Padding point extrapolation techniques for the

Butterworth digital filter. Journal of Biomechanics, 22, 967 – 971.

Winter, D. A. (1990). Biomechanics and motor control of human

movement. New York: Wiley.

Arm swing in vertical jump performance 57