Kinetics and energetics during uphill and downhill carrying of different weights

*Corresponding author. Tel.: 00-45-65-50-34-29; fax: 00-45-66-15-81-86.

E-mail address: [email protected] (G. Sj+gaard)

Applied Ergonomics 31 (2000) 159}166

Kinetics and energetics during uphill and downhillcarrying of di!erent weights

B. Laursen!, D. Ekner!, E.B. Simonsen", M. Voigt#, G. Sj+gaard$,*!Department of Physiology, National Institute of Occupational Health, Denmark

"Institute of Medical Anatomy, University of Copenhagen, Denmark#Center for Sensory-Motor-Interaction, University of Aalborg, Denmark

$Institute of Sports Science and Clinical Biomechanics, Faculty of Health Sciences, University of Southern Denmark,Odense University, Campusvej 55, DK 5230 Odense M, Denmark

Received 5 January 1998; accepted 25 May 1999

Abstract

During physically heavy work tasks the musculoskeletal tissues are exposed to both mechanical and metabolic loading. The aim ofthe present study was to test a biomechanical model for prediction of whole-body energy turnover from kinematic and anthropomet-ric data during load carrying. Total loads of 0, 10 and 20 kg were carried symmetrically or asymmetrically in the hands, while walkingon a treadmill (4.5 km h~1) horizontally, uphill, or downhill the slopes being 8%. Mean values for the directly measured oxygenuptake ranged for all trials from 0.5 to 2.1 l O

2min~1, and analysis of variance showed signi"cant di!erences regarding slope, load

carried, and symmetry. The calculated values of oxygen uptake based on the biomechanical model correlated signi"cantly with thedirectly measured values, "tting to the line >"0.990 X#0.144, where > is the estimated and X is the measured oxygen uptake inl min~1. The close relationship between energy turnover rate measured directly and estimated based on a biomechanical modeljusti"es the assessment of the metabolic load from kinematic data. ( 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Biomechanics; Manual material handling

1. Introduction

Manual material handling includes activities such aslifting, pushing/pulling, and carrying of weights, and hasbeen recognized as being associated with a high preva-lence of musculoskeletal disorders in the workingpopulation. Most extensive are the studies and recom-mendation or legislation on lifting conditions (Christen-sen et al., 1995; NIOSH, 1981,1991), while knowledgeregarding load carrying is sparse. Previous studies onload carrying have mainly used psychophysical or car-diovascular criteria to assess tolerance limits in manualcarrying (see Myles and Saunders, 1979; Holewijn, 1990;Kilbom et al., 1992; Pierrynowski et al., 1981a,b). Thecardiovascular load may also include measurements ofoxygen uptake, which corresponds to the metabolic load.In contrast, for the assessment of acceptable lifting condi-

tions major emphasis is on the mechanical loading. Therehave been few studies of such loadings during load carry-ing (Simonsen et al., 1995; Pierrynowski et al., 1981a,b)although high mechanical forces may occur especiallyduring downhill walking (Kuster et al., 1995). In general,the musculoskeletal tissues are exposed simultaneouslyto mechanical as well as to metabolic loading duringwork and both of these two loading categories must beincluded for setting limits to acceptable exposures in thework place. The metabolic load is due to the activedevelopment of mechanical power by conversion ofchemically bound energy in the muscle tissues under theconsumption of oxygen and accounts for the simulta-neous heat production by including the appropriate e$-ciency. This implies a causal relationship between kine-tics and energy turnover rate in terms of oxygen uptakerate. Theoretically, therefore the metabolic rate can beestimated from kinetic data. Traditionally di!erentmethods are used for quantifying metabolic and mechan-ical loadings, that is oxygen uptake or heart rate forassessing the metabolic load and cinematography andforce recordings in combination with biomechanical

0003-6870/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 3 - 6 8 7 0 ( 9 9 ) 0 0 0 3 6 - 8

Fig. 1. The 12-segment model used for the kinematic calculations. Theweights of the burdens carried were added to the center of mass of thehands.

calculations for the mechanical load. However, in occu-pational "eld studies an important aspect is to keep theinstrumentation as simple as possible, and direct record-ing of oxygen uptake in the workplace is relativelycomplicated. Further, if one set of recordings can givevalid information on the two di!erent loading categories,this has important implications for the quantity of in-formation, which can be obtained for preventive strat-egies. Thus, in case kinematic recordings have beencaptured for biomechanical estimates of joint reactionforces and moments, the same data "le may serve asinput data for estimates of mechanical power and sub-sequently metabolic rate.

The aim of the present study on load carrying was tovalidate estimates of metabolic rate (oxygen uptake) fromthe same basic biomechanical input variables as used forquanti"cation of mechanical loads, i.e. kinematic andanthropometric data.

2. Methods

2.1. Subjects

Six healthy male subjects participated in the experi-ments after giving their oral informed consent to theexperimental procedures. The mean age was 32 years(29}36), height 1.87 m (1.77}1.99), and body mass 81 kg(72}89). The subjects were generally well trained but notsubmitted to any special kind of physical activity.

2.2. Procedure

The subjects were walking lightly dressed on a tread-mill in a temperature-controlled room (&203C) ata speed of 4.5 km h~1 (1.25 m s~1) at horizontal level (L),uphill (U) or downhill (D) the slopes being 8%. The loadsof 0, 5, and 10 kg were carried symmetrically in bothhand(s) comprising total loads of 0, 10, and 20 kg, respec-tively. Additionally, 10 and 20 kg were carried asymmet-rically in one hand only (a). Each of the six subjectsperformed the 5]3 di!erent exercise trials } in random-ized order } two times on di!erent days at least 1 weekapart: one day while the energy turnover rate in terms ofwhole-body metabolic rate was measured directly as oxy-gen uptake, and another day while kinetic data wereobtained from "lm recordings for estimating muscularwork in terms of metabolic task cost as described ingreater detail below (Norman et al., 1989).

2.3. Oxygen uptake and heart rate

Whole-body oxygen uptake was measured in thesteady-state period after approx. 4 min of constant walk-ing. The recordings were obtained by the breath bybreath recording technique (Medical Graphics) and

mean values for 1 min were calculated giving oxygenuptake in liters per min (l min~1). Additionally, heart ratewas recorded continuously and the time synchronizedvalues corresponding to the oxygen uptake data werecalculated.

2.4. Cinematography

High-speed "lm recordings (200 Hz) were obtained forestimating bone-on-bone forces and joint moments aspublished previously (Simonsen et al., 1995,1997). The"lms were converted to video recordings and analyzed bythe Peak Performance System in the semi-automaticmode digitizing re#ective markers. These markers wereglued over bony protuberances corresponding to theestimated axis of the joints in the 12-segment link modelpresented in Fig. 1, and additionally markers delimitingtrunk and head were included. Only one camera wasused which created a condition of hidden points for thelimbs turning away from the camera. This problem wassolved by assuming bilateral symmetry and consequentlyusing the data points from the limb facing the cameraafter shifting them one-half stride cycle out of phase. Onefull stride cycle (with approx. 20 additional frames atbeginning and end accounting for the "ltering e!ect) wasdigitized (50 Hz) for each trial and the data were low-pass"ltered at 5 Hz (fourth-order Butterworth "lter). A 12-rigid-segment link model was used for calculations of thekinetics, where the loads carried were added at the loca-tion of the hands (see Fig. 1). The anthropometric inputdata were depicted from previous studies (Laursen, 1996;Zatsiorsky and Seluyanov, 1983; Plagenhoef, 1971; Demp-ster, 1955). The location of segmental mass centers, vel-ocities, and accelerations were computed directly on the"ltered time position data.

160 B. Laursen et al. / Applied Ergonomics 31 (2000) 159}166

Fig. 2. A sample plot for one subject while carrying 20 kg symmetri-cally at the horizontal level and showing time histories of E

505, E

105, and

E,*/

(see text).

2.5. Calculations

The instantaneous mechanical energy in Joules wascalculated from

E505"+E

105#+E

53!/4#+E

305,

where + is the summation over the 12 segments. Accord-ing to the above equation the energy levels were cal-culated at each instant in time from a summation of thepotential energy, E

105, the kinetic translatory energy,

E53!/4

, and the kinetic rotatory energy, E305

. This impliesthe assumption of energy transfers both between bodysegments and within body segments (Winter, 1990).Changes in the total body energy, E

505, result when work

is done by the subjects. Increases in the curve of theenergy level with time are phases of positive work; de-creases in the curve are phases of negative work. It isassumed that the muscles have to perform both thepositive (slope of E

505'0) and the negative work (slope of

E505(0), and the total muscular metabolic task cost was

calculated according to Norman et al. (1989). For thiscalculation the e$ciency for positive work is set to 25%and for negative work to !120%. The muscular meta-bolic rate (in W) for one trial is then estimated by sum-ming the absolute changes in energy level (E

505) divided

by the respective e$ciencies. A window of one strideduration was scrolled over the full digitized period andthe median value calculated. The minimum and max-imum of this function was approximately within 10% ofthe median value for each trial, which was the data basisfor all further calculations. The total muscular metabolictask cost (in J) for one full stride cycle was then estimatedby multiplying the muscular metabolic rate with strideduration. Conversion of muscular metabolic rate inWatts to whole body oxygen uptake in l min~1 is basedon 20 kJ"1 l O

2and a resting oxygen uptake of

0.2 l min~1, which was added to all individually cal-culated data.

The principle of the biomechanical calculation is givenas an example below for the subject depicted in Fig. 3during uphill walking while carrying 20 kg symmetrically:

One stride cycle is completed in the time interval from0.42 to 1.56 s with a stride duration of 1.14 s. The twophases of increase of the curve during this time periodcorrespond to the positive work, and the sum of the twodelta values amounted to 149 J. Similarly, the two phasesof decrease in this section of the curve correspond to thenegative work and amounted in all to 51 J for this stride.The total muscular metabolic task cost per stride wascalculated by dividing by the respective e$ciencies:149 J (0.25)~1 !51 J (!1.20)~1"639 J.Muscle metabolic rate for task is then:639 J (1.14 s)~1"560 J s~1.This value is converted from J s~1 or W to l O

2min~1:

560 J s~1 (60 s) (20 kJ/l O2)~1"1.68 l O

2min~1.

A resting oxygen uptake of 0.2 l O2

min~1 was addedgiving the total muscle metabolic rate of 1.88 l O

2min~1.

This value was then compared with the direct measuredoxygen uptake which for this particular trial was 1.86 l O

2min~1.

2.6. Statistics

Signi"cant di!erences for slope, load carried, and sym-metry (e.g. symmetric versus asymmetric loading) werecalculated by the ANOVA, and the subjects were in-cluded as blocks. In the case of signi"cance betweensource variables one of the variables was eliminated andANOVA test repeated to reveal di!erence in signi"cance.When testing for symmetry, i.e. for di!erences betweencarrying the load in one hand (asymmetrically) or in bothhands (symmetrically) unloaded walking (0 load condi-tion) was not included. Further, regression lines andcorrelation coe$cients were calculated. The level of sig-ni"cance was set at p(0.05. The relation betweenmeasured and calculated oxygen uptake was analyzedaccording to the method by Brace (1977). In essence, thismethod generates a straight line which minimizes thesum of the squares of the distances of points perpendicu-lar to the line. The slope of the line, A, is the geometricmean of the slopes of the lines which minimize, respec-tively, the sum of the squares of the vertical and thehorizontal distances. The intercept is given byB">!AX, where > and X are the mean values of thevariables.

3. Results

A sample plot of E505

, E105

, and E,*/

is shown in Fig. 2for one subject carrying 20 kg symmetrically at the hori-zontal level. Here E

,*/corresponds to the total kinetic

B. Laursen et al. / Applied Ergonomics 31 (2000) 159}166 161

Table 2Muscle metabolic task cost per stride (in J) calculated from kinematic data as described in the text and given as mean values (range)

Load Downhill Horizontal Uphill

0 kg 150 (90}310) 330 (250}500) 550 (470}700)10 kg, symmetrically 220 (140}330) 320 (260}400) 610 (520}730)10 kg, asymmetrically 190 (160}260) 360 (320}410) 610 (490}770)20 kg, symmetrically 220 (160}290) 310 (260}450) 650 (570}810)20 kg, asymmetrically 250 (130}500) 420 (350}550) 670 (600}840)

Table 1Muscle metabolic rate (W) calculated from kinematic data as described in the text and given as mean values (range)


0 kg 140 (80}290) 290 (220}440) 500 (410}620)10 kg, symmetrically 200 (120}310) 280 (230}350) 540 (460}640)10 kg, asymmetrically 180 (160}250) 320 (270}350) 550 (420}680)20 kg, symmetrically 200 (140}260) 280 (230}400) 580 (510}710)20 kg, asymmetrically 240 (130}480) 390 (320}480) 600 (550}740)

Fig. 3. A sample plot for the same subject as in Fig. 2 while carrying20 kg symmetrically while walking horizontally (as in Fig. 2) as welluphill and down hill and showing the time history of E

505(see text).

energy, i.e. E53!/4

#E305

. For the same subject E505

isdepicted in Fig. 3 for also carrying 20 kg symmetricallyuphill and downhill, respectively. Based on such energycurves of E

505the muscular metabolic rate is calculated as

described in Section 2 individually for each subject. Themean values for the six subjects are presented in Table 1for the 15 di!erent exercise trials. The highest value of

600 (550}740) W was found for carrying 20 kg asymmet-rically uphill, and the lowest value of 140 (80}290) Wduring unloaded downhill walking. Analysis of variancerevealed signi"cant di!erences regarding slope, load, andsymmetry. The stride duration was 1.1 s with a range ofless than 5% and there were no signi"cant di!erencesbetween trials. Total muscular metabolic task cost perstride was the multiplum of muscle metabolic rate andstride duration (Table 2) and showed the same signi"cantdi!erences as Table 1.

Whole-body metabolic rate measured directly as oxy-gen uptake in l min~1 is presented in Table 3. The highestvalue of 2.1 (1.9}2.4) l min~1 was found for carrying20 kg asymmetrically uphill, and the lowest value of 0.5(0.3}0.6) l min~1 during unloaded downhill walking. Asfor estimated muscle metabolic rate signi"cant di!er-ences were demonstrated regarding slope, load and sym-metry. Heart rate was lowest during unloaded downhillwalking (mean: 73, range: 64}80) and highest when carry-ing 20 kg asymmetrically uphill (mean: 130, range:113}152). The heart rate data correlated closely withoxygen uptake (r2"0.778, see Fig. 4) and showed thesame signi"cant di!erences between trial conditions asdid oxygen uptake. The regression line for heart rate (>,in bpm) versus oxygen uptake (X, in l min~1) was>"30.3 X#61, with S.E. for the slope being (1.7) andfor the intercept (2.1).

Comparison of the directly measured oxygen uptake inl min~1 and the muscular metabolic rate estimated fromkinetics, and converted from Watts to liters oxygen up-take per minute as described in Section 2, is shown forone subject in Fig. 5. Here the 15 di!erent trial conditionsare indicated speci"cally. This correlation was signi"cantfor all subjects, the mean r2 being 0.842 and ranging from


Table 3Directly measured oxygen uptake in l min~1 presented as mean values (range)


0 kg 0.5 (0.3}0.6) 0.8 (0.5}1.0) 1.4 (1.1}1.7)10 kg, symmetrically 0.6 (0.4}0.8) 0.9 (0.6}1.1) 1.6 (1.2}1.9)10 kg, asymmetrically 0.7 (0.5}1.1) 0.9 (0.7}1.2) 1.7 (1.3}2.1)20 kg, symmetrically 0.7 (0.5}1.0) 1.0 (0.7}1.3) 1.8 (1.2}2.4)20 kg, asymmetrically 0.9 (0.7}1.1) 1.1 (0.9}1.3) 2.1 (1.9}2.4)

Fig. 4. Simultaneous recordings of measured oxygen uptake (X, inl min~1) and heart rate (>, in bpm) for all trials. The overall regressionline is >"30.3X#61, r2"0.778.

Fig. 5. Directly measured oxygen uptake (l min~1) versus estimatedoxygen uptake (l min~1) from kinematic data (see text) for one subjectidentifying each of the 15 di!erent load-carrying conditions. The line ofidentity is included in the "gure.

0.671 to 0.940. A plot including data for all six subjectsis shown in Fig. 6 together with the line of identity.The regression line including all subjects was:>"0.877 X#283, where X is directly measured and

> is estimated oxygen uptake in l min~1, with S.E. for theslope being (0.051) and for the intercept (63). The overallr2 including all data was 0.784. The line computed tominimize the sum of the squared distances was>"0.990 X#0.144, in concert with Fig. 6, where theline of identity is presented together with all data points.

As seen in Tables 1}3 the ranges for the data betweensubjects are relatively wide. This is in concert with theANOVA showing signi"cance between subjects for thethree variables presented in the tables.

4. Discussion

The most important "nding is the close relationshipbetween metabolic rate measured directly and estimatedbased on a biomechanical model. This justi"es the assess-ment of the energy turnover rate, or oxygen uptake rate,during load carrying from kinematic and anthropometricdata. Mechanical as well as metabolic loads representrisk factors for the development of occupational mus-culoskeletal and/or cardiovascular disorders. In combi-nation, these risk factors may be evaluated reliably fromcinematographic recordings.

4.1. Biomechanical modeling during human locomotion

Estimates of work during human locomotion based onkinematic and kinetic data are numerous since the begin-ning of the 1960s (Cavagna et al., 1963). Unfortunately,these studies mainly deal with horizontal unloaded walk-ing or running, however, the general biomechanical prin-ciples should be taken into consideration from suchstudies. An important aspect in this context is regardingthe relationship between external, internal and totalwork. During walking the total work appears to be lowerthan that calculated from the vertical displacement alone,because of energy transfer. Recently, it has been statedthat the muscle-tendon work of locomotion is most accu-rately measured when energy transfers are only includedbetween segments of the same limb, but not among thelimbs or between the limbs and the center of mass of thewhole body (Willems et al., 1995). This is in line withdetailed calculations and modeling by Aleshinsky (1986),while the method used in the present study implied the


Fig. 6. Directly measured oxygen uptake (X, in l min~1) versus esti-mated oxygen uptake (>, in l min~1) from kinematic data (see text) forall subjects, with separate signature for each subject. The line of identityis included in the "gure.

assumption of energy transfers both between all bodysegments and within segments. Nonetheless, the presentmethod has proven applicable for as di!erent activities asskiing (Norman et al., 1989), bicycling (Wells et al., 1986),and load carrying as in the present study. It is an elegantlysimple biomechanical model, which is easy for practicaluse. Future studies may further validate this model dur-ing other occupational tasks such as pushing and pulling,where force input to the hands is recorded in combina-tion with kinematics.

4.2. Direct measurements of metabolic rate duringdiwerent load-carrying conditions

The absolute values of measured oxygen uptake aresomewhat on the lower side compared with other data inthe literature (Kilbom et al., 1992; Holewijn, 1990). Thismay be due to the method used in the present study, i.e.the breath by breath measurement, instead of using theclassical Douglas bag method. For this reason we deci-ded to also use a rather low value of 0.2 l min~1 forresting oxygen uptake to be added to the calculatedmuscle metabolic rate for conversion to whole-body oxy-gen uptake. It should be pointed out that the presentbiomechanical model probably is not suitable to depictsubtle di!erences in metabolic rate. But under conditionswith large di!erences in work load, like in the presentstudy with more than 4-fold di!erences, signi"cant rela-tionships are found between measured and calculatedmetabolic rate. For occupational settings such sensitivityof a method may well be su$cient when work loads areto be evaluated on a group level, that is when evaluatingthe task and not individual di!erences.

When walking at a horizontal level the magnitude ofthe loads carried had a relatively small in#uence on the

energy turnover rate which in the present study may bedue to maximal load being only 20 kg. When carryingfrom 35 to 70 kg metabolic cost increased, although itshowed no signi"cant changes when expressed per kgload (Soule et al., 1978). However, the present studyshowed that, walking uphill with a load of only 10 kg,energy turnover rate increased by more than 70% com-pared with carrying 10 kg horizontally and uphill walk-ing almost doubled the value when carrying 20 kg.Interestingly, in absolute terms the energy turnover ratewas reduced relatively when walking downhill. This is inconcert with a study on concentric and eccentric bicyc-ling (Wells et al., 1986). The explanation for this "ndingis, that the internal work which the muscles have toperform to move the limbs relative to the center of massof the whole body is of the same order of magnitudeduring uphill (concentric) and downhill (eccentric) workand only dependent on stride frequency (pedal rate). Thisinternal work must in both conditions be added to theexternal work performed which therefore increases theconcentric and decreases the eccentric total externalwork rates.

4.3. Empiric formula for prediction of metabolic rate

Prediction of energy consumption may also be basedon an empirically developed formula by Pimental andPandolf (1979), which includes the variables: body mass,load mass, walking velocity, and grade. However, suchcalculations cannot di!erentiate between, e.g. di!erentmodes of carrying the load, which has been reported tobe of signi"cance (Balogun, 1986; Datta and Rama-nathan, 1971). The lowest relative values have beenreported for carrying head-supported loads as the Sherpaof the Himalayas or East African women (Heglund et al.,1995). Interestingly, in the present study we could dis-criminate between symmetrical and asymmetrical weightcarrying, the metabolic rate being signi"cantly about10% higher during asymmetrical than during symmetri-cal carrying, which could not have been identi"ed by theempirical formula.

The metabolic cost in oxygen uptake per kg mass(body#load) per meter of translocation was 0.133 mlO

2kg~1 m~1 or 2.67 J kg~1 m~1 during the horizontal

walking in the present study. This is in concordance withdata on running in the order of 0.179 ml O

2kg~1 m~1,

since energy demand during running is somewhat higherper mass per distance than during walking (Di Pramperoet al., 1986). In the present study, this value was indepen-dent of the load carried which is in contrast to estimatesfrom the above-mentioned empirical formula, whichwould predict an increase in metabolic cost per kg withincreased load (Holewijn, 1990). Interestingly, the meta-bolic cost per kg per m actually decreased when subjectswere running while loaded (by 10% of body weight orapprox. 7 kg) with sandbags evenly distributed around


the upper body (Bourdin et al., 1995). This implies thatthe mode of carrying the load as well as the speed oflocomotion must be taken into account when identifyingthe most e$cient way of transporting materials man-ually.

4.4. Recommendation of permissible occupational limits

In the literature di!erent percentages of oxygen uptakeare considered acceptable during occupational settings,for reference see Holewijn (1990) and Kemper et al.(1990). In general, for a whole 8 h working day therecommended maximum permissible limit for energyturnover rate is 30% of the maximum capacity, for 4 h40%, and for 2 h 50% (Waters et al., 1993). The datapresented in Table 3 almost exclusively depend on bodymass, since the e$ciency between subjects is similar, andtherefore the relative load is mainly dependent on theworkers maximal oxygen uptake rate. In the population,maximal oxygen uptake decreases with age and ranges atthe age of 20 years roughly from 2 to 5 l min~1 but at theage of 60 years from 1 to 3 l min~1 (As strand, 1960). Basedon the present data, large parts of the population will notbe able to carry more than 10 kg horizontally and willnot be able to walk uphill for 2 h at the actual slope andspeed even without carrying any external burden. Walk-ing uphill imposes unequivocally the highest metabolicload on the worker, the metabolic rate being highest forthis condition even without any external loading. Thesubjects in the present experiments were quite "t youngmales and they could only sustain the 20 kg uphill forrelatively few minutes. In fact, during horizontal walkingwhile carrying 20 kg the oxygen uptake was less thanduring unloaded uphill walking. This emphasizes that theslope of the terrain must be taken into account whensetting acceptable maximum limits for load carrying.

The whole-body metabolic rate, however, may not bethe only important variable limiting performance duringhorizontal load carrying. Here a number of experimentsindicate, that no more than 10 kg can be recommendedfor young healthy men when the task is to be performedfor prolonged periods of time (Holewijn, 1990; Kilbomet al., 1992). This is consistent with the present data andtheir kinetic counterparts in a previous study where hipbone-on-bone forces in the order of 6.4 kN were reported(Simonsen et al., 1995), which is far beyond the actionlimit of 3.4 kN for low back compression forces and closeto the corresponding maximum permissible limit of6.5 kN (NIOSH, 1981). During downhill load carryingthe metabolic load is seen to be of the least importance,and for this condition kinetic variables must be includedfor evaluating acceptable loads. Large joint momentshave been reported especially in the knee even duringunloaded downhill walking and may explain problemsduring, for example, anterior cruciate ligament de"ciency(Kuster et al., 1995).

5. Conclusions

Methodological implications: A simple biomechanicalmodel can be used for the assessment of both metabolicand mechanical loading of the musculoskeletal systemduring load carrying. However, further experiments areneeded to validate to what extent this model can be usedduring other manual material handling tasks.

Practical implications: (1) The slope of the terrain hasa profound e!ect on the metabolic rate during weightcarrying; (2) the weight carried is of special signi"cancefor the metabolic rate during uphill walking; and(3)asymmetric location of the weight carried increases, ingeneral, the metabolic rate by 10%.

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