Applied Ergonomics 33 (2002) 485–491

Oxygen consumption, heat production, and muscular efficiencyduring uphill and downhill walking

Arthur T. Johnson*, M. Benhur Benjamin, Nischom Silverman

Biological Resources Engineering, University of Maryland, College Park, MD 20742, USA

Received 13 November 2000; received in revised form 1 September 2001; accepted 1 February 2002

Abstract

Oxygen consumption, heat production, and muscular efficiency for walking are parameters important to know for ergonomics

models and equipment design. Most of these assume that the oxygen consumption and heat production of downhill walking are the

same as for uphill walking.

Eight subjects wearing insulating clothing walked on a treadmill at three uphill and three downhill grades, and at level grade at a

rate of 1.1m/s. Oxygen consumption ’VO2 was calculated from steady state measurements of respiratory minute volume and oxygen

percentage. Heat production ð ’qÞ was calculated from the rate of heat storage in the body and clothing. Least-squares best fit

equations for oxygen consumption and heat production found were to be ’VO2 ¼ 0:813þ 0:0361G þ 0:000810G2 � 0:0000302G3 and

’q ¼ 6:55þ 0:185G þ 0:0114G2 � 0:000190G3 where G is percent grade. Approximations show that ’VO2 (downhill)=0.5 ’VO2

(uphill), ’q (downhill)=0.67 ’q (uphill), and muscular efficiency Z (downhill)=�2Z (uphill). r 2002 Elsevier Science Ltd. All rights

reserved.

Keywords: Walking; Energetics; Negative work

1. Introduction

Mathematical modeling of ergonomic processes canbe used in the design of protective clothing, respiratorymasks, and life support systems (Givoni and Goldman,1972; Johnson and Dooly, 1995). It is important in thesemodels to know how much oxygen needs to be suppliedto the working individual, and how much excess heatmust be removed. Designs based on these models shouldbe roughly optimized such that too much capacity isavoided because of the additional weight that itrepresents, and too little capacity is avoided because ofits threat to life or work performance.

These models may include walking up a grade as acomponent of the metabolic load of an individual, butdo not include the metabolic costs of walking down theother side of a hill. Astrand and Rodahl (1970) showedthat the energy expenditure of a muscle undergoingnegative work is about one-sixth that of a muscle doingthe same amount of positive work. Johnson (1991)

concluded that walking uphill should probably producetwice as much heat as walking downhill.

In the prescription of walking exercise, energyexpenditure of downhill walking must be known. If anexercising individual is to include uphill and downhillwalking, how does this compare to the same distance onlevel ground?

Over the years a number of investigators haveobtained experimental data relating uphill and downhillwalking. Chauveau (1901) observed that oxygen con-sumption for positive treadmill work (uphill) wasapproximately twice as much as negative treadmill work(downhill). Karpovich (1959) showed that one-third ofthe energy was required to walk downstairs compared toupstairs, but he did not indicate that the rates of ascentor descent were equal. Muscular efficiencies for thewalking downhill approach 120% (McMahon, 1984)—suggesting that muscles absorb more energy whenwalking downhill than they expend during level walking,Wanta et al. (1993) showed that energy cost wasminimal at grades between �6% and �15%, butincreased at grades more and less steep.

Hesser (1965) studied the energy expended by 10 maleand female subjects walking up and down a staircase 1m

*Corresponding author. Tel.: +1-301-405-1184; fax: +1-301-314-

9023.

E-mail address: aj16@umail.umd.edu (A.T. Johnson).

0003-6870/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 0 3 - 6 8 7 0 ( 0 2 ) 0 0 0 3 1 - 5

high with both up and down treads. Two differentspeeds were used, yielding external work rates of 14.7and 26.7 klbm/min/kg of body mass. At the lowerspeed, the ratio of oxygen costs for positive to negativework approximated 8:1, and the ratio at the higherspeed was 5:1. He concluded that there was a differencein the type of work done walking up stairs and thatwalking down stairs.

Laursen et al. (2000) also measured oxygen consump-tions of individuals walking uphill and downhill to testthe predictive ability of their biomechanical model ofoxygen consumption based on kinematic and anthro-pometric data. Their main objective was to predictoxygen consumption when carrying loads either symme-trically or asymmetrically in the hands while walkingeither horizontally or up and downhill at an 8% slope.They concluded from their data that their model wassufficiently accurate for their purposes.

For modeling or engineering purposes, oxygen con-sumption, physical work rate, and heat production arethree parameters that may need to be predicted. Yet,previous studies have not provided this information in amost useful form. Most studies have not convertedoxygen consumption into physical work rate nor havethey determined rate of heat production. Hence therewas a need to generate data suitable to human systemsmodeling and engineering application.

Given the range of speeds, grades, and protocols usedby previous investigators, the objective of this researchwas to obtain comparative data for oxygen consump-tion, physical work rate, and heat production for peoplewalking at a constant speed for several different uphilland downhill grades. There was no attempt in this studyto separate energy expenditures of men and women, norto investigate effects of added loads or walking speeds.

2. Methods

Four male and four female subjects between the agesof 18 and 35 years volunteered for this study. Subjectheights were 173710.8 cm (mean7std. dev) and masseswere 70.4711.2 kg. The protocol was approved by theUniversity of Maryland Institutional Review Board.

Subjects filled out a health history questionnaire andsigned a consent form. A verbal orientation to thetesting was given. Heights and weights were recordedbefore testing. Subjects walked on a motor driventreadmill (Quinton Q65) at a constant speed of 1.11m/s and at seven randomly ordered grades of 0%, 75%,715%, and 725%. Respiratory measures of tidalvolume, minute volume, and exhaled fractions of oxygenand carbon dioxide were taken each minute. Measure-ments of core temperature, skin temperatures, and heartrate were made every 3min until body core temperatureincreased by 0.51C. At that time the test session was

stopped and walking time was noted. Each test sessionwas conducted on a different day.

Subjects were clothed to prevent significant heat lossby conduction or evaporation. All subjects wore lightunderwear, a 3mm thick neoprene wet suit (BodyGlove; Redon, CA), and US Army fatigues. They alsowore sneakers, socks, and two pairs of gloves; the innerpair was made of latex and the outer pair was thickleather welding gloves. A neoprene hood loosely coveredthe head and a US Army M17 full facepiece respiratormask covered the face. Wearing this outfit allowed bodyheat production (corrected for respiratory losses) to becaptured as stored body heat. Also, thermoregulatorymechanisms such as vasodilation and sweating wouldquickly become saturated and the body mass storingheat would be constant.

Negative grades were obtained by elevating the rearend of the treadmill using a three step wooden stand.Respiratory ventilation was measured with a Fleisch #3pneumotach (OEM Medical; Richmond, VA) andValidyne DP-15 (Northridge, CA) differential pressuretransducer and a Validyne CD-12 transducer indicator.Calculations were performed with a custom computerprogram (Johnson and Dooly, 1993). Oxygen usage andcarbon dioxide production was monitored with aPerkin-Elmer (St. Louis, MO) model 1100 medical gasanalyzer.

Four YSI (Yellow Spirngs, OH) Precison 4400 Seriesskin surface temperature sensors were used to measureskin temperatures at the chest, arm, thigh, and calf(Benjamin, 1997; Ramanathan, 1964). A YSI Precision4400 Series rectal probe inserted 12 cm beyond the rectalsphincter was used to constantly monitor body coretemperature. Leads from skin and rectal sensors wereconnected to a 10-channel switch box connected to aYSI Precision 4000A telethermometer.

3. Calculations

Oxygen consumption was calculated from (Johnson,1991):

’VO2 ¼ ’VE 1� FEO2 � FECO2ð ÞF1O2=F1N2

� �� FEO2

� �

¼ ’VE 1� FEO2 � FECO2ð Þ0:2093=0:7904� ��

� FEO2; ð1Þ

where ’VO2 is the oxygen consumption, (l/min), ’VE theminute volume, (l/min), FEO2 the fractional concentra-tion of oxygen in the expired breath (unitless), FECO2

the fractional concentration of carbon dioxide in theexpired breath (unitless), FIN2 the fractional concentra-tion of nitrogen in the inspired breath (unitless).

The weight of clothing worn by the subjects was2 kg, and it was desired to modify the results to bevalid for unclothed or lightly clothed subjects. Oxygen

A.T. Johnson et al. / Applied Ergonomics 33 (2002) 485–491486

consumption was corrected for the weight of clothingworn by the subjects by calculating predicted metabolicwork using the Pandolf equation for treadmill walking(Pandolf et al., 1977):

’M ¼ 0:15wb þ 0:102wbðð1:5v2 þ 0:35vGÞ

�WbvG=100Þ; ð2Þ

where ’M is the metabolic rate (kJ/min), wb is thebody weight including clothing (N), v the speed ofwalking (1.1m/s), and G the grade of walking surface(percent).

’M was calculated for the body weight with ð ’MclÞ andwithout clothing ð ’MÞ; and corrected oxygen consump-tion was calculated assuming a linear relationshipbetween metabolic work and oxygen consumption:

’VO2ðunclothedÞ ¼ ’VO2ðclothedÞ ’M= ’Mcl: ð3Þ

Bodily heat production for these insulated subjectswas assumed to be related to heat storage, andrespiratory heat losses through

’q ¼ ’Sb þ ’Scl þ ’Eres þ ’Cres; ð4Þ

where ’q is the body heat production (kJ/min), ’Sb therate of body heat storage (kJ/min), ’Scl the rate of heatstorage in clothing (kJ/min), ’Eres the rate of respiratoryevaporative heat loss (kJ/min), and ’Cres the rate ofrespiratory convective heat loss (kJ/min).

Body heat storage was calculated as

’Sb ¼ mbcpbðDTb=DtÞ;

where mb is the body mass (kg), cpb is the specific heat ofbody tissues (3.47 kJ/kg1C), and DTb=Dt the rate of riseof body temperature (1C/min).

Clothing heat storage was calculated similarly byusing clothing mass, specific heat of the clothing (2200 J/kg1C for neoprene), and average clothing temperaturemidway between measured skin temperature and ambi-ent temperature.

From Johnson (1991):

’Eres ¼ H ’VEraðores � oaÞ; ð5Þ

where H is the latent heat of evaporation of water (kJ/kg), ra the density of air (kg/l), ores the humidity ratio ofwater saturated air at core body temperature (kg H2O/kg air), and oa the humidity ratio of ambient air (kgH2O/kg air).

’Cres ¼ ’VEracpaðTrect � TaÞ; ð6Þ

where Trect is the rectal (core) body temperature (1C),and Ta the ambient temperature (1C).

The metabolic rate, or physical metabolic costof the exercise, was calculated from (Gagge and Nishi,1983)

’Mcl ¼ 21:14 ’VO2ð0:23RQþ 0:77Þ; ð7Þ

where RQ is the respiratory exchange ratio (unitless).

The external work rate was calculated from (Aoyagiet al, 1995)

’Wcl ¼ 0:06mtotgv sin y; ð8Þ

where ’Wcl is the external work rate wearing clothing(kJ/min), mtot the mass of body plus clothing (kg), g theacceleration due to gravity (9.81N/kg), and y the angleof inclination with respect to the horizontal (=arctanG/100, degrees).

The muscular mechanical efficiency was calculated inthe standard fashion

Z ¼ ’Wcl= ’Mcl; ð9Þ

where Z is the muscular efficiency (unitless).

4. Results

Respiratory minute volume and oxygen consumptionreached steady-state after about 4min for many of thetest sessions. However, an upward drift in the oxygenuptake was observed for negative grades among sixsubjects. This observation was consistent with thosereported in the literature (Klausen and Knuttgen, 1971;Knuttgen et al., 1982; Byrnes et al., 1985; Dick andCavanagh, 1987), and is called the slow component ofoxygen uptake. The slow component has been attributedto physiological factors that reduce muscular efficiencyand require recruitment of additional muscle fibers.

Oxygen consumption values used in subsequentcalculations were taken, where possible, to avoid theslow component. Oxygen consumption values werechosen that appeared to have reached a steady statebefore the secondary upward drift occurred. Forinstances where no steady state was reached, especiallyat the �25% grade, the maximum value of oxygenconsumption was used.

In Fig. 1 are seen plots of mean body temperaturewith time for one subject at all grades walked. Anaverage rate of rise was determined from the data forcalculations of body heat storage.

Table 1 contains the important results of thisexperiment. In the table is found oxygen consumptioncorrected for the weight of clothing worn and applicablefor an unclothed or lightly clothed person. Actualmetabolic rates ð ’MclÞ uncorrected for the weight ofclothing appear in the table. Calculated metabolic, orphysiological, work rate values ð ’MÞ corrected forclothing weight are also given in the table. Comparingthe value of 15.64 kJ/min for walking on the level(0% grade) with the range of values of 11.1–22.2 kJ/minfor walking on the level at 1.34m/s (Johnson, 1991)shows good agreement between this result and apreviously published value.

Heat production rate is given. Heat storage in theclothes worn was found to be 7–20% of the total.

A.T. Johnson et al. / Applied Ergonomics 33 (2002) 485–491 487

Muscular efficiencies vary from �59% for �25% gradeto 29% for 25% grade. The negative muscular efficiencyvalues for negative grades reflect the negative externalwork being performed by the muscles as they lower thebody with each step.

Metabolic rate should equal external work rate plusrate of heat production. Webb et al. (1988) indicated

that some work performed during walking is involvedwith such things as compression and bending the solesof the shoes. For this study there would also be addedthe work of moving the stiff clothing. Therefore, there isa component of external work rate that is not part of thegross work of moving a mass up or downhill. Subtract-ing the rate of heat production ð ’qÞ from the metabolic

Fig. 1. Mean body temperature response with time.

Table 1

Results from this study. Values are means7standard deviations

Grade (%) ’VO2 (l/min) ’Mcl (kJ/min) ’M (kJ/min) ’Wcl (kJ/min) ’WD (kJ/min) ’q (kJ/min) Z (%)

�25 0.8770.33 18.8575.80 17.6375.43 �11.1370.81 7.12 11.7372.38 �59

�15 0.6270.20 13.5772.27 12.7573.61 �6.7970.46 5.84 7.7371.91 �50

�5 0.6170.20 12.7974.19 12.3974.05 �2.297016 7.25 5.5471.89 �18

0 0.7670.17 16.6777.18 15.6472.35 0 10.46 6.2170.70 0

5 1.0670.24 23.0373.77 21.6073.54 2.2970.14 14.04 8.9971.28 10

15 1.4570.39 31.8278.03 29.5877.47 6.7970.48 19.34 12.4873.52 21

25 1.7470.46 37.7576.69 35.5176.55 11.1370.77 22.79 14.9672.70 29

’VO2 denotes oxygen consumption for an unclothed or lightly clothed person.’Mcl denotes metabolic rate wearing clothing.’M denotes metabolic rate corrected to unclothed or lightly clothed subjects.’Wcl denotes external work rate for clothed subjects as tested in this study.’WD denotes difference between metabolic rate and heat production for clothed subjects.

’q denotes actual heat production rate.

Z denotes muscular efficiency.

A.T. Johnson et al. / Applied Ergonomics 33 (2002) 485–491488

rate ð ’MclÞ yields a larger value of work rate ð ’WDÞ than’Wcl: All values of ’WD are positive, and remain nearly thesame for all negative grades and increase with grade forpositive grades. The differences between ’Wcl and ’WD

would, presumably, be equivalent to the rate of workdone by the subjects on the environment, which cannoteasily by accounted for.

A statistical analysis (ANOVA) testing the hypothesisthat the rate of heat storage is the same for all gradeswas rejected at the p ¼ 0:05 level. Coefficients ofdetermination (R2) for linear relationships relating meanbody temperatures with time for individual tests rangedfrom 0.83 to 0.98. No statistically significant genderdifferences were found for rate of heat storage.

In Fig. 2 are shown oxygen consumption data plottedwith a least-squares best fit (R2 ¼ 0:937) cubic poly-nomial equation:

’VO2 ¼ 0:813þ 0:0361G þ 0:000810G2

� 0:0000302G3: ð10Þ

For heat production, ð ’qÞ; the best fit (R2 ¼ 0:880) cubicpolynomial is (Fig. 3)

’q ¼ 6:55þ 0:185G þ 0:0114G2 � 0:000190G3: ð11Þ

5. Discussion

Downhill to uphill ratios of oxygen consumptionyielded mean values of about 50%, indicating that about

half as much oxygen was utilized while doing negativework as when doing positive work. This finding is inharmony with the results obtained by Chauveau (1901),Orsini and Passmore, 1956, and Pivarnik and Sherman(1990), but in conflict with the results of Karpovich(1959), who indicated that only one-third the energy wasrequired during negative work when compared topositive work. However, no indication was given byKarpovich whether his observations were made at equalspeeds. Asmussen (1953), Abbott and Bigland (1953),and Hesser (1965), had observed changes in oxygenuptake ratios with speed. Asmussen and Abbott hadindicated an increase in oxygen uptake ratios with anincrease in speed, while Hesser had observed a decreasein oxygen ratios with an increase in speed. Since in thecurrent investigation all experiments were performed atthe same speed, they shed no light on the disagreementbetween the results of Asmussen and Abbot versusHesser.

Upon examination of the oxygen consumption duringnegative work, an upward drift in the oxygen uptakewas observed. This upward drift was noticeable at�25% grade (0.9370.35 l/min). Oxygen uptake at thisgrade was about 15% more than at level walking. Thisresult is consistent with results reported in the literature(Klausen and Knuttgen, 1971; Knuttgen et al., 1982;Byrnes et al., 1985; Dick and Cavanagh, 1987).

Somewhere around �5% or �15% grade was themost efficient walking in terms of oxygen cost. Wantaet al. (1993) estimated that the most economical grade

Fig. 2. Oxygen consumption ð ’VO2Þ data plotted with least-squares best fit line and approximations. Values are means with standard deviation bars.

A.T. Johnson et al. / Applied Ergonomics 33 (2002) 485–491 489

lay between �6% and �15% and Minetti et al. (1993)observed it to be at �10%. The results of this study donot conflict with either of the previous findings.

Least-squares equations for oxygen consumption andheat production appear in Figs. 2 and 3. These appear tofit the data reasonably well and can be used to find themost efficient walking grades. Differentiating Eq. (10)results in a minimum oxygen consumption at a grade of�13%. Of course, the grade corresponding to theminimum oxygen usage probably varies somewhat fordifferent individuals.

A very useful result of this experiment would berelatively simple equations for oxygen consumption andheat production that could summarize the data and beused for modeling or design purposes. Because eachperson’s responses are highly variable and differ fromthe responses of others, high precision coefficient valuesmay not be warranted compared to the ease of use. Fourequations summarize these results, with the first twoapplied to uphill walking and the next two applied todownhill walking: uphill (zero grade not included):

’VO2 ¼ 0:9þ 0:03G; ð12Þ

’q ¼ 7:7þ 0:3G; ð13Þ

downhill (compared to uphill):

’VO2downhill ¼ ’VO2=2; ð14Þ

’qdownhill ¼ 2 ’q=3: ð15Þ

Values calculated from these equations differ from theexperimental data averages by no more than 12%, andmost differences are well within 10%. These equationsare plotted in Figs. 2 and 3 and labeled as approxima-tions. Although they do not fit the data as well as thepolynomials, they are much simpler and may beadequate for many purposes.

Other readers may wish to split the data differently. Ithas been suggested that the �25% grade is a special casedue to the extra balance required. Different interceptsand coefficients are obtained for the linear Eqs. (12)–(15) if the data is grouped differently, but the utility ofthis approach still lies in its simplicity.

As an example of the potential use of these equations,Givoni and Goldman (1972) developed a model topredict military heat casualties based on temperature,environment, and clothing. Their predictions used heatproduction of downhill walking to be equivalent to thatproduced by uphill walking. If they had adjusted theirdownhill heat production according to Eq. (15), thentheir predictions would have been more accurate. BothEqs. (14) and (15) can also have utility for designingsystems to support firefighters, people walking on otherplanets, and respiratory protective equipment used byworkers in industry and agriculture (Johnson et al.,1992a). Johnson et al. (1992b) showed that taskperformances based on dexterity, cognition, and motorskills degrade as body temperature increases. Modelsto predict these performances will be required forbetter equipment design or for better management of

Fig. 3. Heat production rate ð ’qÞ plotted with least-squares best fit line and approximations. Values are means with standard deviation bars.

A.T. Johnson et al. / Applied Ergonomics 33 (2002) 485–491490

individuals performing these types of tasks. For thesepurposes, Eqs. (12)–(15) provide the required computa-tional ability in forms to obtain useful results.

What this study has accomplished is to give informa-tion in a useful form that can be used to calculateoxygen consumption and heat production for engineer-ing purposes. Simple extensions of Eqs. (10)–(15) can beperformed using methods appearing in the literature(and appearing in the calculations section of this paper)to calculate values applicable to other exercise and workconditions.

6. Conclusions

Values for oxygen uptake, heat production, andmuscular efficiencies were obtained for uphill anddownhill walking by eight subjects. The results showthat downhill walking requires only half the oxygen andproduces two-thirds as much heat as does uphillwalking. Life support systems designed for peoplewalking uphill and downhill using these results can besized smaller than by assuming equal oxygen uptake andheat production rates.

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