REVIEW mt. J. Sports Med. 7 (1986) 55—72Georg Thieme Verlag Stuttgart New York

The Energy Cost of Human Locomotion on Land and in Water*

P.E. di Prampero

Département de Physiologie, C.M.U., 1 • rue Michel-Servet, Genve, Switzerland

55

1 Foreword

The number of persons regularly devoting a significant frac-tion of their leisure time to physical exercise has vastly in-creased in the last decades, as has the knowledge of thebasic physiologic mechanisms underlying human motion.The time seemed therefore ripe, for practical and theoreti-cal reasons, to summarize our present ideas on the ener-getics of human locomotion on land and in water.

The aim of this article is that of subsuming under a coherentpicture the large collection of data dealing with human loco-motion, rather than that of providing an extensive reviewof the literature. Thus, even if I hope not to have forgottenany basic papers, I wish to apologize for facts and theorieswhich may have escaped my attention.

2 The Founders

Obviously enough, the earlier attempts to describe theenergetics of human locomotion in quantitative terms weredevoted to walking. Indeed, as early as the second half tothe 19th century, Smith (1859) Gruber (1891), Katzenstein(1891), and Sonden and Tigerstedt (1895) measured theenergy cost of level walking at speeds between 3.2 and 4.8km h'. Their values, ranging between 0.32 and 0.51 kcalkg km1 are astonishingly close to the actually acceptedones. At the beginning of the 2nd decade of this century,Bresina and Kolmer (1912) and Bresina and Reichel (1914)had established that the energy cost of walking, per unit oftransported weight and of distance, increases sharply above4.8 km h. Katzenstein (1891), Schumburg and Zuntz(1896), and Loewy et al. (1897) investigated the energycost of uphill walking and calculated its efficiency from theratio of potential energy change to metabolic energy ex-penditure, obtaining values ranging from 20% to 37%.Galeotti et al. (1914) determined the energy cost of walkingat the altitude (2900 m) of the "Laboratorio A. Mosso" onthe Col d'Olen (Mount Rosa); the value they obtained(0.37—0.55 kcal kg km1) was in the range of those ob-tained by others at sea level.

The energy cost of running was determined by Wailer (1919)and by Liljestrand and Stenström (45), whose values variedbetween 0.8 and 1.3 kcal kg km, again not far fromthe presently accepted ones, while Hill (31) was probablythe first to study the effects of air resistance in running.

* This study was supported in part by the Swiss National Fundof Scientific Research, grant No. 3.364.082.

A very extensive study on the energy cost of walking andrunning was undertaken by Margaria (48) who investigatedspeeds between 0.5 and 9.5 km h and slopes between+40% and —40% in walking, and between 6.5 and 15 km• h'and +5% and —30%, in running, respectively. Margaria'sdata will be summarized in the appropriate section (4.1 .3).The reader is referred to his extensive study for a completereview of the literature on walking and running up to 1938.

The physiology of swimming was extensively investigatedby Liljestrand and Stenström (44) and by Liljestrand andLindhard (42) who determined gas exchange, heart rate,blood pressure, and cardiac output on subjects swimmingthe breaststroke at speeds between 1 and 3 km h. Ac-cording to their data, the energy cost per unit distance in-creased with the speed from 28.5 ml 02 m1 (at 1.2 kmto 49.1 ml 02 m (at 3.0 km li) for a 90-kg subject,while it was independent of the speed (between 1.2 and2.4 km h') and amounted to 42 ml 02 m for a smallersubject (51 kg). These authors were also the first to ob-serve a different energy cost of swimming, once referred tothe body size, between men and women. In addition, theyalso investigated the relationship between passive towingforce and speed. Karpovich and Millman (36) investigatedcrawl, backstroke, breaststroke, butterfly, and the now lesscommon sidestroke at speeds between 2.5 and 6.1 kmTheir values, however, are grossly too large as comparedwith the currently accepted ones because of their over-estimate of the 02 debt contracted during the actual swim-ming period. In previous studies, Karpovich (35) and Karpo-vich and Pestrecov (37) had also measured the relationshipbetween the passive towing force and the speed. Otherauthors, cited by Karpovich and Millman, who studied swim-ming energetics include Greene (1930), Schmelkes (1935—1936), and Egolinskii (1940).Beside the physiology of walking, running, and swimming,Liljestrand and Stenström (45) and Liljestrand and Lind-hard (43) also investigated some aspects of cross-countryskiing and of rowing. This last was also discussed in somedetail by Henderson and Haggard (30).

At the turn of the century, Zuntz (77) investigated in depththe energy requirement for recreational cycling. Zuntz alsocompared the speed attained, with a given 02 consumption,during cycling and walking. According to his data, with an02 consumption (resting included) of 1.0 1 minm ,thespeeds attained were 4.8 and 9.6 km h in walking andcycling, respectively, and reached 7.5 and 18 km h' withan 02 consumption of 2.0 1 min'. Thus, cycling appearedto be '-2.5 times more economical than walking. Benedictand Cathcart (4) studied the efficiency of cycling; they were

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56 mt. J. Sports Med. 7 (1986) P.E. di Prampero

the first to assert what is now commonly held, i.e., that theoptimal pedal frequency is on the order of 1 Hz.

After this brief historical survey, the stage is now set for amore detailed analysis of the energetics of human locomo-tion.

3 introduction and Definitions

The record speeds attained in different forms of humanlocomotion range, for endurance events of similar duration,from about 1.7 ms1 (6.1 kmh)in free style swimmingto about 14 m s (50.4 km• h') in cycling (Table 1). Thereasons underlying these vastly different performancesreside essentially in the energy cost of locomotion, definedas the amount of energy (above pre-exercise resting) spentper unit distance. Throughout this article, the energy costof locomotion will be given its own symbol, C, and will beexpressed in J 'm' (or kJ km1 )*.The close relationship existing between the performanceand the energy cost of locomotion can be explicated asfollows. The energy expenditure above resting per unit oftime (metabolic power, E) is the product of the speed oflocomotion (v), times the energy cost (C):

ECvRearranging Eq 1, and applying it to maximal conditions

max = Emax c-' (2)it can be easily shown that the maximal speed depends onthe ratio of the maximal metabolic power (Emax) to theenergy cost of locomotion at that speed. Thus, since Emaxis about the same for all groups of elite athletes, the maximalspeed attained in the different forms of locomotion is setessentially by the value of C, being high in those forms inwhich C is low and vice versa (Table 1).

Equation 2 applies regardless of the sources, aerobic oranaerobic, supplying the energy for muscular contraction;it becomes particularly useful, however, in aerobic condi-tions in which Emax can be identified with the subject'smaximal 02 consumption (VU2 max), an easily measurablevariable. Hence, in aerobic conditions Eq. 2 becomes:

vam = F 02max C1 (3)where vamax is the maximal aerobic speed and F the maxi-mal fraction of VO2max that can be sustained throughoutthe duration of the effort in question. It is well known, infact, that VO2max cannot be sustained for periods ex-ceeding '—25 mm (41). Hence, beyond this durationF < 1.0, (12) to attain 0.6 for exercise duration of 5—6 hin well-trained subjects (41). However, according to Davies(17), ultra-long distance runners can sustain a higher frac-tion of V02 max, up to 0.66 for an exercise duration of8 h.

* The consumption of 1 ml of 02 in the human body yields 20.9 Jat a RQ = 0.96. This equivalence will be assumed to hold through-out, thus neglecting the minor effects of RQ. (The energy equi-valent of 02 consumption ranges from 19.6, for RQ = 0.71, to21.1, for RQ = 1.0, J - ml).

Distance

(km)

Recordtime

(s)

Recordspeed(m-s')

C

(kJ - km')

Swimming (free style) 1.5 894.56 1.677 1400Competitive walking 3.0 788.09 3.807 356Running 5 780.40 6.407 300Speed-skating (ice) 10 874.33 11.437 175Cycling 10 713.20 14.021 160

The three quantities F. 'c'o2max, and C, combined as inEq. 3 explained '—j 70 % of the variablility of performance ina group of long-distance runners (21). In these same subjects,V02 max alone explained about 50 %, and in combinationwith F or C about 60 %, of the overall variability. Hence,Eq. 3 can be considered a satisfactory description of theenergetics of endurance running.It seems therefore legitimate to extend the validity of Eq. 3

(1) to all forms of human locomotion in which the drivingenergy is metabolic and which are sufficiently standardizedso as to make the use of a single average value of C meaning-ful.

An additional practical advantage of Eq. 3 is to show sepa-rately the effects of the physiologic (numerator) and tech-nical (denominator) aspects of tl1e performance. For ex-ample, Eq. 3 shows that an increase in maximal aerobicspeed resulting form a given type of training can be mean-ingfully interpreted if, and only if, the changes of the threeterms of the equation can be separately assessed. Indeed,since changes in opposite directions of the numerator anddenominator of Eq. 3 can offset each other, only the know-ledge of the individual values of the three terms of theequation allows the appropriate training strategy.

The preceding paragraphs have hopefully shown the theo-retical and practical importance of a precise knowledge ofthe energy cost of locomotion. This will now be discussedin some detail for the most common forms of human loco-motion on land and in water.

4 Terrestrial Locomotion

The major part of this chapter (4.1) is devoted to an analy-sis of the energy cost of walking, running, speed skating andcycling. A final short section (4.2) will deal with the ener-getics of cross country and alpine skiing.

4.1 Walking, Running, Speed-Skating, CyclingThe effects of air resistance, a common characteristic in allforms of terrestrial locomotion will be considered first(4.1.1). This will be followed by an analysis of the specificaspects of the above types of locomotion (4.1.2), and of theeffects of the environmental conditions, and of the size andshape of the body on performance (4.1.3).

Table 1 World records and corresponding speeds for aerobic eventsof comparable duration (from about 12 to about 15 mm) in theindicated types of locomotion. Overall energy cost (C) for a 70-kg,175-cm male subject is also indicated (see appropriate sections forfurther details).

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The Energy Cost of Human Locomotion on Land and in Water mt. 3. Sports Med. 7 (1986) 57

k' (Js2m3)(m2

CNA (J m kg)

C (Jm)Cx

4.1.1 Air Resistance

In all forms of human locomotion on land, the air resistance(Ra) is proportional to the square of the air speed (v):

Ra k V2 (4)

where k is a constant which depends on the air density, thedrag coefficient, and the area projected on the frontal plane(see 4.1.3 b).The air resistance (a force) can be viewed as the mechanicalwork performed per unit distance against this force. Hence,the metabolic energy spent per unit distance to overcomethe air resistance or drag (CR) is given by:

CR k' v2 (5)

where the constant k' = k i, r being the mechanical effi-ciency of work performance against the air drag.

In turn, the metabolic power spent against the air (ER) isgiven by the product of CR times the ground speed (i):

ER=CRS=k'V2 cosawhere a is the angle between air and ground speed. Through-out this article, we will deal only with locomotion in calm airso that wind and air speed are equal (v ) and a = 0. Hencecos a = 1.0 needs not be explicated and will be omitted;Eq. 6 reduces therefore to:

ER = k' v3

The constant k' is approximately the same for all fourtypes of locomotion considered here (see Table 2). Forspeed-skating and cycling (on standard racing bikes), thisis strictly true only if the subject assumes the most aero-dynamically favorable position, i.e., with the trunk parallelto the ground.

This rather unexpected finding may well be fortuitous; itsresult, however, is rather straightforward. The metabolicpower utilized against the air resistance (a) at a given speedis the same regardless of the type of terrestrial locomotionconsidered here (see Fig. 2), and (b) at the record speedsreported in Table I for typically aerobic events, it is widelydifferent in walking, running, speed-skating, and cycling,amounting, for a 70-kg, 175-cm subject, to 0.06, 0.19,1.18, and 2.08 kW, respectively. Hence, since the maximal

power of the athletes competing in the above events issimilar and does not greatly exceed 2.0 kW*, the fractionof power spent against nonaerodynamic forces is very large(90%, or greater) in walking and running, intermediate inspeed-skating, and rather minor (10% or less) in cycling.Indeed, as it will become apparent in the next paragraph,this last is the most "intelligent" form of locomotion since,thanks to the saddle which supports and stabilizes the body,it reduces to a minimum the energy waste against nonaero-dynamic forces. This allows employment of very nearly allthe metabolic power of the subject against the air resistance,thus attaining speeds greater than in any other form ofhuman locomotion.

4.1.2 Energy Expenditure Against NonaerodynamicForces

As pointed out in the previous paragraph, in the forms oflocomotion considered here, the fraction of the overallmetabolic power utilized against nonaerodynamic forces' at world record aerobic speeds varies by a factor of 20, ormore, being maximal in walking and minimal in cycling.The following factors underly the nonaerodynamic energyexpenditure: (1) potential and kinetic energy changes dueto the oscillations of the center of mass of the body in thevertical plane and to its acceleration (deceleration), at each

(6') stride (in walking, running and skating); (2) friction of theskate blade or of the wheel with the terrain (in skating andcycling); (3) internal work, i.e., work not leading directlyto changes of position of the center of mass of the body(e.g., when an arm is projected forward and the other back-ward as in running); (4) muscular contractions for the main-tenance of posture; (5) the work of the respiratory musclesand of the heart.These different factors will not be separately analyzed inthe course of this article; the energy expenditure due to thesum of them all will be defined as nonaerodynamic energyexpenditure and given the symbol CNA, when expressed perunit of distance, and ENA, when expressed per unit of time.

* 1 kW = 1.36 HP is the metabolic power corresponding to an 02consumption of about 48 ml 02 per second.

Table 2 Constant k' (J m3 and per m2 of body surface), nonaerodynamic energy cost above resting (CNA, J m and per kg body weight),total energy cost above resting for a 70-kg, 175-cm-subject (C), and drag coefficient (Cx) for indicated types of terrestrial locomotion. Data re-fer to PB = 760 mmHg,T = 20°C, fIat and uniform terrain, in absence of wind. For further details see 4.1.2 and 4.1.3. For references see legend

to Fig. 1.

Competitive Running Speed-skating Bicyclingwalking on ice

"dropped posture"standard racing bike

"dropped posture"

0.46 0.40

1.43 + O.91v 3.86

100 + 64v + 0.83v2 270 + 0.72v2

1.10 1.10

0.44 0.43

1.00 0.17

70 + 0.79v2 13 + 0.77v2

0.65 0.75

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58 mt. 1. Sports Med. 7 (1986) P.E. di Prampero

Fig. 1 Energy cost above resting per Unit of distance, C (J' m orml 02 m') as a function of the speed (m' s' ) fora 70-kg, 175-cmsubject at sea level (PB = 760 mmHg) in calm air at 20°C on flatuniform terrain. w. = Natural walking; c.w. = competitive walking;r. = running; c.c.s. = cross-country skiing ("double pole", snowtemperature —3°C); s.s. = ice-speed-skating (dropped posture>;c. cycling (standard racing bike, dropped posture). Lower curvesindicate nonaerodynamic energy cost, upper curves overall energyCost. Hence, distance between the two is the energy cost againstaerodynamic forces. In natural walking, this last is so small that thetwo functions are practically superimposed; in cross-country skiing,the aerodynamic energy expenditure is not precisely known. Sinceboth coordinates are logarjthmic, all points characterized by the samemetabolic power output (E = Cv = constant) lie on the same straightline with slope = —1: log C = log constant — log v. The two iso powerlines indicated correspond to the maximal aerobic power of a nonath-letic subject and of an elite endurance athlete. The points of inter-section between an iso power line and a given function define themaximal aerobic speed for the power and the type of locomotionconsidered (see also text and Fig. 2). From data of di Prampero etal. (23, 24); Margaria (48); Margaria et al. (49); Pugh (57); Saibeneet al. (61). For interindividual variation of C, see Fig. 3 and Table 3.

CNA, indicated in Fig. 1 as a function of the speed for thevarious forms of locomotion considered here (see also Table2), is essentially independent of the speed in running (18,28, 39, 48, 49, 50, 56, 69), speed skating (23), and cycling(15, 24, 58).In walking, CNA is relatively high at low speeds, attains aminimum, equal to about half the value for running, be-tween 1 and 1.4 m' s, and increases again at higher speeds(5, 13, 18, 48, 59). It is interesting here to note that, ata speed greater than 7.5 to 8km• h1, CNA is larger for walk-ing than for running; hence, above this speed, running is moreeconomical. Interestingly enough, uninformed subjectschange spontaneously from walking to running or vice versaat, or close to, this speed. The same is true, even in moresophisticated form, for those animals, such as dogs andhorses, characterized by three forms of locomotion (gait,trot, and gallop): the transition from one to another occursalways at that speed at which the chosen form of locomotionbecomes more economical.

Competitive walking seems to be a compromise betweennatural walking and running. Indeed, for speeds greaterthan 7.5 km h', CNA in competitive walking, thoughlarger than in running (28,51), is definitely smaller than

Fig. 2 Thin lines indicate overall metabolic power output aboveresting (kW. or 102 min1) as a function of the speed for a 70-kg,175-cm subject in the same conditions and the same types of loco-motion, with the exception of cross-country skiing, as in Fig. 1.Thick line (ER) indicates metabolic power utilized against the airresistance, equal in the four forms of locomotion considered anddrawn on the basis of the average k' as from Table 2. Verticaldistance between curve ER and thin lines indicates power utilizedagainst nonaerodynamic forces. Horizontal dotted line is the maxi-mal aerobic power of an elite endurance athlete; correspondingspeeds, as defined by the intersections between dotted and thinlines, are indicated by arrows. The fraction of energy spent againstthe air resistance at maximal speeds is represented by hatched barsin appropriate columns.

what could be expected from an extrapolation of thecurve for natural walking (Fig. 1).

The frictional losses in the transmission system and in theaxles of a good bike are very minor (76). Hence, in cycling,CNA depends essentially on the type of the terrain and ofthe tires: tires of greater section and lower inflation pres-sures yielding larger values of CNA (19). The values reportedin Fig. 1 and Table 2 apply to standard competition tires (in-flation pression 7 to 8 atm) on smooth solid terrain. Onvery smooth surfaces (linoleum or polished wood), CNAattains values about half (15) and on macadamized roadsabout twice (58) those reported here.

The value of CNA for speed skating (Fig. 1 and Table 2)has been obtained by extrapolating to speed =0 the observedlinear relation between total energy cost and v2 (23). Assuch, it is presumed to include all factors independent ofair resistance which, however, cannot be analyzed separately.For further details and references on the biomechanics ofspeed-skating, the reader is referred to the work of vanIngen Schenau and co-workers (70, 71, 72).Knowledge of the overall energy cost per unit of distance,as given by the sum of the energy spent against air resist-ance plus that spent against nonaerodynamic forces (C =CR + CNA) (Fig. 1 and Table 2) allows calculation of themetabolic power necessary to proceed at a given speed, to-gether with its partition in the two components (aerodyn-amic and nonaerodynamic) (Fig. 2). Furthermore, Fig. 2also allows calculation of the maximal speed attained witha power output of 1.8 kW above resting (5.171 02 nun4),

E(kW)

00 5 10 15

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The Energy Cost of Human Locomotion on Land and in Water mt. J. Sports Med. 7 (1986) 59

Table 3 Energy cost of locomotion above resting (C) together with correspondingSD in absolute and relative terms are reported for the indi-cated forms of locomotion at the indicated speed. CV coefficient of variation; n = number of subjects. References: natural walking, see Fig. 3;running, di Prampero et al., (211; speed-skating, di Prampero et al. (23), competitive walking and cycling, unpublished observations.

Naturalwalking

Competitivewalking

Running(road)

Speed-skating(ice)

Cycling(velodrome)

C(J'kg 'm

2.3 4.8 3.7 2.1 1.2

SD(J• kg' m'

0.35 0.35 0.3 0.15 0.08

CV1%)

15 7 8 7 7

v(ms')

1.25 3.5 3.6 10 9.6

n 21 5 36 5 7

I I2 3 4 5

v, kmhFig. 3 Energy cost of walking above resting per kg body weight (Cw)as a function at the speed in normal subjects (open dots, n 21) andin patients suffering from multiple sclerosis (black dots, n indicated).Average values SE. For normal subjects, SE was within the thick- -ness of the dot, amounting on the average to 0.007 ml °2 kg' m l

(Olgiati and di Prampero, in press).

corresponding approximately to the maximal aerobic powerof an elite endurance athlete. It amounts to about 4.52,6.17, 10.84, and 13.49 (m s'),in competitive walking,running, speed-skating, and cycling, respectively, ratherclose to the corresponding record speeds reported in Table1 for aerobic events. At these speeds, the fraction of energyspent against nonaerodynamic forces is about 95%, 90%,40% and 10% of the total, respectively. These considera-tions show quantitatively that an improvement of the aero-dynamics of walking and running would not lead to anymajor improvements of performance; on the contrary, itis greatly beneficial in skating and even more so in cycling.This last point will be dealt with in the next paragraph.

Fig. 4 Pedal frequency (Hz) as a function of the mechanical poweroutput (we, kW) in cycling. Iso metabolic power lines (kW; 1 kW

2.87 I 02 min I are also indicated, thus allowing assignment toany given point of the plane of one single efficiency value (fl). Thepoints characterized by r = 22%, 23%, 24%, and 25% are joint byiso-efficiency lines (24); from data of Banister and Jackson (3) andSeabury et al. (65).

Before turning to this, however, a few comments as to theinterindividual variability of C seem to be appropriate. Thedata reported in Figs. 1 and 2 and in Table 2 are averagevalues obtained on well-trained subjects of good, but notexcellent, technical ability. In Table 3, the values of C fornatural and competitive walking, running, speed-skating,and cycling at the speeds indicated are reported togetherwith the corresponding SDs. These appear to be rathersmall (from about 7% to about 15% of the overall energycost), indicating that these forms of exercise are not verymuch affected by interindividual variations due to trainingand/or other technical factors. It must be pointed out,however, that the data on competitive walking, skating,

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60 mt. J. Sports Med. 7 (1986) RE. di Prampero

and cycling were obtained on homogeneous groups oftrained athletes, a fact which obviously tends to level offinterindividual differences.

Natural walking, spontaneous as it is, is also characterizedby small interindividual variations (Table 3 and Fig. 3).These, however, when expressed in percentage of the over-all energy cost, are larger than in the other forms of locomo-tion considered in Table 3. In addition, some forms ofdiseases, which disrupt neuromuscular coordination and/ormuscle tone to a large degree, lead to a marked increase ofthe energy cost of natural walking (Fig. 3), a fact whichis partially reversible with appropriate training (67).

The energy cost of running per unit body weight anddistance (C) is essentially the same in men and women (8,26) and in sedentary and athletic subjects (1, 11, 49). Somerecent observations, however, suggest that C is about 10%larger in sprinters than in long-distance runners (34). Inchildren, C is larger than in adults (14), the difference de-creasing with increasing age, to attain the adult value at15—16 years of age (47). According to Mac Dougall et al.(47) in fact, C amounts to 5.05, 4.66, 4.27, and 4.08J kg' 'm on the average (above resting) in children of7—9, 10—12, 13—14, and 15—16 years of age at speeds of9.3, 10.2, 11.4, and 12.3km h1, respectively. Thesevalues are to be compared with an average of 3.9 J kg m1in adult men (Table 2). In addition, the data of Mac Dougallet al. (47) show that: (1) also in children C (above resting)is essentially independent of the speed and (2) the coeffi-cient of variation of C in children is about twice that ob-served in adults and reported in Table 2.

The energy cost of running attains a minimum at an optimalstride frequency which does not change or increases onlyslightly with the speed (6, 32, 39). Also in cycling, as it iswell known, the mechanical efficiency, and hence the energycost of transport, is affected by the pedal frequency. Thedata from various authors (3, 65) summarized in Fig. 4show that the optimal frequency increases from 0.7 to1.0 Hz with increasing the mechanical power output from50 to 300 W. However, throughout the whole range ofpedal frequencies, the efficiency varies only from about22% to about 25%.

In the light of Eqs. 2 and 3, the data reported in Table 3show that the variability of C can be expected to have aconsiderable effect on top performance in sports, wheredifferences of a fraction of 1% may often be crucial. In-deed, the interindividual variability of C accounts for about13% of the variability of performance in amateur runnerscompeting in a long-distance events (21 or 42.195 km)(21).

4.1.3 Environmental Conditions, Body Size, and Shapea Incline of the GroundThe energy cost of walking and running uphill or downhillis well known from several sources (5, 18, 48, 49, 57). Theresults of the detailed studies of Margaria (48) and ofMargaria et al. (49) are summarized graphically in Fig. 5.These data show that: (1) the energy cost of walking has aminimum at an optimal speed which is smaller the steeper

Fig. 5 Energy cost above resting of walking at the optimal speed,and of running (C, J kg m l), as a function of the incline (i, %)of the terrain. Every point on the abscissa is characterized by agiven value of work performance against gravity per unit of distance.This allows construction of iso-efficiency lines (six of which appearon the graph) along which the ratio mechanical work/energy cost isconstant. For downslopes, efficiency is negative since the mechani-cal work is performed by the gravitational field on the subject'sbody. (Note that the efficiencies, as calculated here, neglect the factthat the subject moves along the hypotenuse of a right angle triangle,the ratio of whose catheti expressed in percent constitutes the in-cline of the terrain. 1-lowever, for the slopes considered here, theerror does not exceed 4.5%). The energy cost of running is inde-pendent of the speed at all slopes, that of walking is not. This lastis indicated in the insert as a function of the speed, for different ivalues. From Margaria (48) and Margaria et al. (49).

the slope, whereas (2) at all slopes, the energy cost of runningis independent of the speed (not shown in Fig. 5); (3) the en-ergy costs of walking and running have an absolute minimumat a slope of about —10%, being higher on both sides of thistrough; finally, (4) at all slopes, the energy cost of walkingat the optimal speed is less than that of running (about halfin the range from 0 to —10%).

These data apply to treadmill walking or running; as such,they do not include the effects of air resistance which, how-ever, at the speeds considered here, is very small (16, 50, 56,57). It can then either be neglected or taken into accountwith the aid of Table 2.

The additional mechanical work done per unit distanceagainst gravity when cycling uphill is given by: M g i, whereM is the mass of the subject + bike, g the acceleration ofgravity, and i the incline of the terrain as given by thetangent of the angle (a) between the terrain and the horizont-al (i = tan a)*. (It should be noted here that the slope in % isequal to i x 100). The energy required to perform this extrawork is given by: M g i where i is the mechanical effi.ciency of cycling. Assuming for simplicity i 0.25 (but seeFig. 4) and giving g its absolute value (9.81 m s.2),theenergy for slope climbing, per unit distance (J . rn'1), isgiven by: 39.2 Mi.* Strictly speaking, since the subject is moving along the hypo-

thenuse of a right angle triangle, the work done per unit dis-tance is given by M g sen n. However for a < 16° tan a sen awithin an error <4%.

-20 -tO1%

0 20 30

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The Energy Cost of Human Locomotion on Land and in Water mt. J. Sports Med. 7 (1986) 61

The effects of upsioping terrains on the energy cost of cyc-ling can then be easily taken into account by adding thisterm to the value of C reported in Table 2 which becomesthen:

C=0.17M+0.43SAv2 +39.2Mi (7)

where SA is the subject's body surface area. This equationapplies when riding a conventional racing bike on smoothterrain, in "dropped posture," for PB =760 mmHg andT 20°C (the effects of barometric pressure and tempera-ture changes will be discussed later).

For downsloping terrains, i is negative; under these condi-tions the third term of Eq. 7 represents the energy equivalentmade available by gravity. This can be used against the otherforces opposing motion (air and ground friction); thus, Eq. 7allows calculation of the wind speed attained during a freewheel descent on a known slope. For example, the constantfree wheel speed attained by a 70-kg, 175-cm subject(SA = 1.8 m2) riding a 7-kg bike on a —10% slope (i —0.1)can be calculated by setting C 0 in Eq. 7. It amounts to19.31 ms' (69.53 kmh').Equation 7 also allows calculation of the maximal slope onwhich a subject can ride a bike provided that: (1) his maxi-mal metabolic power is known and (2) the speed is assigneda minimum value below which equilibrium cannot be main-tained. To facilitate this type of calculation, a nomogram hasbeen constructed (Fig. 6) which shows that if the minimalspeed is tentatively given a value of 1 m s_I (3.6 km• h'),the maximal slope a subject can climb with a VO2maxabove resting of 43 ml 02 kg1 min1 (15 W kg1) is about42% and increases to about 70% for a VO2max of 63 m1 kgt

mind above resting (22 W - kg1), where the power is ex-pressed per kg total weight (subject + bike). It goes withoutsaying that these performances would be possible only onsmooth terrain and with the use of an appropriate gearsystem allowing optimal pedal frequencies even a very slowspeeds.

b Air DensityAn immediately intuitive strategy for reducing the effectsof the air resistance is to move in the wake of somebody (orsomething) proceeding at the same speed. This strategy iswidely applied in cycling, but running is no exception. Intrack running at 6 m s, such a procedure leads to a reduc-tion of metabolic power equal to that obtained by reducingthe speed by about 0.1 m 51(15,40, 57). The effects ofshielding are obviously larger in cycling. It has been shownin fact that, when proceeding at racing speed closely in thewake of one another, cyclists can reduce their power outputby about 30%, thus increasing their speed by about 0.9—1.8m s_i (40).The extreme example of this state of affairs is the incrediblespeed of 223.13 km h1 attained over a distance of 1.2km by A. Abbott (USA) in 1973 by pedaling a bike in thewake of a specially prepared car.

Besides the above shielding effects, the energy expenditureagainst the air density is affected also by the barometricpressure and hence by the altitude above sea level. This pointwill be dealt with in the paragraphs that follow.

Fig. 6 This nomogram allows calculation of the metabolic powerrequirement above resting per kg weight tbody + bicycle) whencycling uphill once the speed and the angle of the terrain with thehorizontal (o) or the corresponding incline Ii = tan o) are known.Alternatively, the nomogram can be used to obtain the maximalslope that can be climbed by a subject whose Emax is known andprovided that the speed be assigned a minimal value. The effects ofwind resistance at the speed and slopes considered here are very small(< 1.0%) and have been neglected.

It has been previously stated (4.1.1) that the energy spent,per unit distance, against the air resistance increases with thesquare of the air speed. The porportionality constant be-tween these two variables, k' in Eq. 5, is a function of thearea projected on the frontal plane (Ap), the air density (p),and the efficiency of work performance (n):

k' = 0.5 Cx Ap p (8)where the drag coefficient (Cx), which depends on the shapeof the object, is constant within the range of speeds con-sidered here. For a detailed analysis of this subject, thereader is referred to Pugh (57).The effects of air density, and of Cx and Ap, on k', and henceon the energy cost of locomotion, will be briefly discussedin this section and in the next one, respectively.

The air density is directly proportional to barometric pres-sure (PB) and inversely proportional to absolute tempera-ture (T), as described by:

p =0 0.359 PB T' (9)

where 0.359 = 273/760, PB is given in mmHg, I in °K, andp0 = 1.293 kg m3 is the air density at 760 mmHg and273 °K. (The effects of air humidity on air density are verysmall and will be neglected). Moreover, for a given tempera-ture, PB decreases with the altitude above sea level (km), asdescribed by:

PB = 760 e°27 km (10)

0.0

0

E

Wkg5

IC

Is

20

010

0 l

120 00

3.5

V

m

3.0

25

2.0

15

10

0.5

0

0 30

01.020

25

25

30

1.0

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0 2000 4000Altitude Cm)

Fig. 7 Maximal 02 consumption, percentage of the sea level value,a function of barometric pressure (PB) or altitude above sea level.

The decrease of V02 max is the same in acclimatized (full symbols)or unacclimatized subjects (open symbols). From Boutellier et al. (7).

Fig. 8 Maximal speed attained in aerobic conditions during ice-speed-skating (vmax, s-s.) and cycling (vmax, cy) at the indicated altitude.Speed values were calculated assuming a Va2 max of 1.8 kW aboveresting at sea level (5.17102 min) and constant temperature of20°C and are expressed relative to sea level. Other conditions as inTable 2 and Fig. 1. Relative decreases of V02 max and of air densityat constant temperature (p) are also indicated.

Table 4 Maximal speeds attained at sea level (s.l.)1 and at the optimal altitude in aerobic conditions during ice-speed-skating and cycling.Values calculated assuming two widely different VO2max's at sea level: 1.1 and 1.8 kW above resting, corresponding to 3.16 and 5.17 I min',respectively. Other conditions as in Fig. 1 and Table 2. Relative increases of speed are also reported.

Sea level Optimal altidudevamax altvamax sI.max

kWVamaxm . s_I km

'O2 maxkW

vamaxm

Cycling1.101.80

10.7612.85

3.03.5

0.961.49

11.5413.84

1.0721.077

Ice.speed-skating

1.101.80

8.5810.94

2.02.5

1.031.64

8.7811.37

1.0231.039

Therefore, the values of k' reported in Table 2 can be cor-rected for any given altitude and temperature with the aidof Eqs. 8—10.

The above considerations show that, because of the decreaseof k', and hence of the energy requirement to overcome theair resistance, the speed attained with a given metabolicpower can be expected to increase with altitude. However,also the maximal 02 consumption decreases with altitude(Fig. 7). Therefore, the maximal aerobic performance willbe the net result of two conflicting processes: decrease ofair resistance tending to improve performance and fall ofV02 max tending to reduce it.

It can be shown that, up to a given altitude, the decrease ofthe energy expenditure against the air resistance is greaterthan that of V02 max, this leading to an increase of per-formance; for greater altitudes, the opposite is true. The op-timal altitude can be calculated provided that the subject'sVU2 max and the partition of the overall energy expenditurebetween aerodynamic and nonaerodynamic factors is known:

it is close to sea level for walking and about 750 m forrunning, for which the improvement in performance isnegligible. For speed-skating and cycling, the improvementin maximal aerobic performance, for an athlete whosemaximal aerobic power at sea level is 1.8 kW above resting,attains 3.9% and 7.7% of the sea level values at the idealaltitudes of 2500 and 3500 m, respectively. For a nonathlet-ic subject, the gain to be expected is less (2.3% and 7.2%)and is attained at slightly lower altitudes, 2000 and 3000 m,respectively. These considerations, summarized in Fig. 8and Table 4, are consistent with the present world recordfor 1 h unaccompanied cycling, obtained by F. Moser atMexico City (2230 m a.s.l.) with 51,152 km in January1984. They do show, however, that, for an athlete of hisclass, better performances could be expected at an evenhigher altitude.

In this context, it is interesting to calculate that the maximalspeed an athlete of the power of Moser could attain at PB= 0 exceeds 500 km' h1. Obviously enough, this is a purely

62 mt. J. Sports Med. 7 (1986) P.E. di Prampero

100

90

80

700

60

50

40 600 PB(torr) 400

0 2 km 6

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Table 5 Metabolic power above resting per unit weight , W kg(in brackets ml 02 kg ' min1) for indicated type of locomotionand speed for two subjects of extremely different body dimensions:subject 1, 50 kg, 150 cm; subject 2, 100 kg, 200 cm. Ratio betweenthe two powers is also reported. Values apply to conditions specifiedin Fig. 1 and Table 2.

v(ms)

Subject 1 Subject 2Subject 2Subject 1

Running 6 26.2(75.1)

25.7(73.9)

0.98

Speed-skating 11 27.7(795)

24.9(71.5)

0.90

Cycling 13 28.6(82.1)

24.1(69.1)

0.84

Fig. 9 The "Vector single" (see also Table 6). Permission of Du Pontde Nemours International S.A., Geneva, is gratefully acknowledged.

Table 6 Principal characteristics and performances of some man-powered vehicles. CR= coefficient of rolling resistance; this last is given by theproduct of CR times the overall weight. Cx = drag coefficient. The maximal speeds indicated correspond to a mechanical power of 1 HP (0.734kW), 2 HP for tandems, at a 20°C temperature on flat uniform terrain at the indicated altitude. Well-trained male subjects can develop a mech-anical power of about 1 HP for approximately 30 s. Hence, the indicated speeds are realistic estimates of performance over a 200-rn sprintwith flying start (modified from Grosset al. (27)].

Vehicleweight

(kg)

CR C Frontalarea

(m2)

Sea level

Maximal speedkm h2230m 3600m

(Mexico City) (La Paz)

Europeanconventionalbike C

18 0.006 1.10 0.51 45.4 49.6 52.7

Racing bike"fullydropped"

7 0.004 0.75 0.44 54.9 60.0 63.7

Tandem

Vector

(threewheels)

19

31

0.005

0.005

1.00

0.11

0.48

0.43

60.3

100.8

66.3

110.0

70.2

116.2

Vectortandem(three wheels)

* 34 0.005 0.13 0.44 118.9 129.8 136.9

theoretical calculation since such an achievement will neverbe feasible in actual practice because of the many obviousobstacles. It does show in clear-cut terms, however, the roleplayed by air resistance in cycling.

c On Size and ShapeThe energy spent against the air resistance is a function ofthe area projected by the moving object on the frontalplane (Ap, Eqs. 5 and 8), hence the natural tendency toassume, especially at high speed, the position yielding theleast possible value of Ap, given the constraints of the typeof locomotion in question. For the sake of simplicity, inthis article we will deal only with locomotion in a stand-ardized position. The interested reader is referred to Baak

and Binkhorst (68) and to van Ingen Schenau et al. (72) foran analysis of the above type of problems. During terrestriallocomotion in a standardized position, as it is here thecase, Ap can be assumed to be proportional to the bodysurface area (SA). On these grounds, therefore, the coeffi-cient k' (Eq. 8) has been expressed in Table 2 per unit sur-face area.As a first approximation, humans can be viewed as solidsof similar shape and equal density; hence, Ap can be as-sumed to increase with the square of the linear dimensionof the body, while the body weight increases with the cubeof the same dimension. Larger subjects can therefore be ex-pected to have a lesser Ap per unit body weight than smal-ler subjects, and hence to attain greater speeds with a given

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64 mt. 1. Sports Med. 7 (1986) P.E. di Prarnpero

power output per unit body weight. This difference isnegligible in walking and running: it is, however, appre-ciable in skating and cycling, as indicated in Table 5 fortwo subjects of extremely different size. Thus, because ofpurely anthropometric reasons and neglecting other factors,such as thermoregulation for instance, cyclists and skatersof larger body sizes can be expected to perform better, fora given maximal power per unit body weight, than theirsmaller colleagues. Obviously enough, this difference be-comes less crucial when cycling uphill because of the de-creasing effects of wind and the increasing effects ofgravity.The effects of the object shape on the air resistance is meas-ured quantitatively by the term Cx of Eq. 8. This is re-ported in Table 2 for standard conditions in walking, run-ning, speed-skating, and cycling. In the first three forms oflocomotion, no attempts have been made to reduce Cx byartificial means, with the obvious exception, for skating, ofmaintaining the trunk as parallel as possible to the terrain.In cycling, on the contrary, a vast number of data havebeen collected on the effects of several types of streamlinedcoachworks (see Fig. 9) and/or cycling postures on energyexpenditure and maximal speed. Some of these data aresummarized in Table 6, mostly from a recent article byGross et al. (27) to which the interested reader is referredfor further details. These data show that the maximal speedsattainable in level cycling can, theoretically, well exceed100 km h'. Again the best performances are to be ex-pected at altitudes of 3000—4000 m. In actual practice,the maximal speed attained with a streamlined vehicle (theVector Single, see Fig. 9) over a 200-rn strech with flyingstart is 94.75 km h1 (D. Grills, USA, 1980) to be com-pared with the corresponding world record speed of 71.287km h' on a standard racing bike (L. Heisslich, 1985).

4.2 Cross-Country and Alpine Skiing

The energy expenditure during cross-country skiing can begreatly affected by upslopes and downslopes, as well as bythe weather and snow conditions. We will therefore consideronly the energy cost of cross-country skiing on flat terrain,in the absence of wind and for well-defined and constantsnow temperature. Under these conditions, the energy costof "double pole" cross-country skiing is described by (61):

C = 38 + 33.3 F + 2.8 v2

where C is given in J m for a 70-kg man, F is the fric-tion of the ski, and v the speed in m s1. In turn, F is givenby the product of the subject's body mass (in kg) times acoefficient which depends on the temperature of the snow(0.03 5 for —2°C and 0.07 for —15°C). Thus, the effects ofthe temperature of the snow are rather large: in the aboveexample, in fact, for a speed range from 2 to 5 m s, anincrease of the snow temperature from —15° to —2°C yieldsa decrease of C on the order of 30%—40%.

Equation 11 shows that, for a snow temperature of —2°C,the energy cost of cross-country skiing is less than for run-ning at moderate speeds, but tends to approach it as thespeed increases (Fig. 1). Saibene et al. (61) have also shownthat, in all conditions, the energy cost of the "diagonal pole"technique is greater than that of the "double pole."

It should finally be pointed out that the only term of Eq. 11which has a precise physiologic meaning is the one repres-enting the energy expenditure due to the friction of theskis (33.3 F). The other quantities entering into the deter-mination of C cannot be separately obtained from theabove equation, which has therefore a purely descriptivemeaning.

Alpine skiing cannot be standardized to any meaningfulextent. In addition, in this case, the driving force is theweight of the subject, and the energy expenditure is utilizedto properly control the descent. As such, it goes beyondthe limits of this review. We will therefore only mentiontwo recent studies on slalom and giant slalom (62, 73),which have shown that the rate of energy requirement dur-ing laps of 55—75 s exceeded the subjects' VO2max, at-taining 75—95 ml 02 kg' mm' for national level skiersand about 60—70 ml 02 kg1 m1n1 for instructors. Theinterested reader is referred to the above two papers forfurther information and references.

S Aquatic Locomotion

The water resistance, or drag, is the major force to be over-come during aquatic locomotion. Since the density of thewater is about 800 times that of the air (998.2 vs 1.205kg m3 at 20°C and 760 mmHg), this requires a largeenergy expenditure. In addition, in most forms of aquaticlocomotion, the overall efficiency of progression is ratherlow (10% or less). Both these factors lead to large energycosts of transport, and hence to low maximal speeds(Table 7). The aim of this section is to discuss in somedetail the energetics and biomechanics of swimming androwing.

5.1 Swimming

5.1.1 "Good" vs "Bad" Swimmers and Different StrokesThe energy cost for swimming the front crawl is independ-ent of the speed, up to about 0.9 m s1 and amounts to0.57 0.085 (SD) kJ m1 and per m2 of body surface area(SA) in male swimmers of good technical ability (collegeswimmers); in poor swimmers, it is higher, attaining 0.88

0.24 (SD) kJ m5 and per m2 SA in sedentary men (25,

(11) 55). At greater speeds, C increases to attain 0.85 kJ m1per m2 SA at 1.4 m ' s' in college swimmers (Fig. 10).In addition, elite swimmers are characterized by a value ofC, which is on the average about 40% lower than that ofcollege swimmers (Fig. 10), a fact which underlines theimportance of a correct technical training for improvingperformance -

The energy cost of the different types of strokes is reportedin Fig. 11 for a group of elite swimmers, from the data ofHolmér (33): the most economical stroke is the crawl, fol-lowed by the backstroke. At the other extreme is the dol-phin, the breaststroke being closer to the crawl at low speedand to the dolphin at high speed. It should be noted herethat in swimmers of poor technical skill, the breaststroke,at a speed of 0.3—0.5 m s, is about 30% more econom-ical than the front crawl. It may then be concludedthat the breaststroke is "more natural" than the crawl so

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Table 7 World records and corresponding speeds in free style swimming and running (men), for events of comparable duration. Indicatedenergy costs above resting (C) apply to a 70-kg, 1 75-cm man at sea level and 20°C temperature. For running, these include the initial accelera-tion phase, accounting for about 8%, 3.3%, 1.2%, and 0.2% for the 400 to 1500 m distance, respectively. For swimming, the reported energycosts are 10% less than observed during constant speed swimming (see Fig. 11) because of the (estimated) contribution of the initial dive andof the push on the wall of the pool at each 50-rn stretch during competitive swimming.

Swimming Running(free style) (track)

Time(s)

Distance(km)

Speed(m s' ) (kJ

C -' km ' )Time

(s)Distance

(km)Speed

(m s ' )C

(kJ km'

48.95 0.1 2.043 1900 43.86 0.4 9.120 0.360107.44 0.2 L862 1450 101.73 0.8 7.864 0.325227.80 0.4 1.756 1250 209.45 1.5 7.162 0.310894.56 1.5 1.677 1170 780.40 5.0 6.407 0.300

Fig. 10 Energy cost above resting of swimming the front crawl perm2 of body surface in men (kJ m' o ml 02 m) + college swim-mers Ifrom Pendergast et al. (55)1; elite swimmers Ifrom Holmér(33)]; • elite swimmers (Pendergast, di Prampero, unpublished ob-servations). The dotted square at 2 m s was calculated estimatingthe maximal amount of energy elite swimmers can derive fromaerobic and anaerobic (lactic and alactic) sources in 50 s over 100 mdistance. For college swimmers, the coefficient of variation of Camounted to 15% in the investigated range of speeds.

stroke.

5.1.2 Of Women and MenIn noncompetitive swimmers, the energy cost of the frontcrawl at 0.9 m - s1 is about 30% less in women as comparedwith men, provided that the difference in body surface istaken into account, amounting to 0.88 0.24 and to 0.63

0.19 kJ ' m1 per m2 SA (± SD), respectively (55).

This unexpected finding, already observed by Liljestrandand Stenström (44), is due to the different distribution ofbody density along the head.feet axis in women and men.In fact, when a human body lies in water, the thorax tendsto float, while the legs and the feet tend to sink. This gen-erates a torque, given by the product of the underwaterweight of the feet, times the distance feet-center of air (55).Women have, on the average, greater fat depots at the but.

tocks and thighs and shorter and less muscular lower limbsthan men. Since fat is less dense than water, whereas musclesand bones are heavier, women are characterized by a lessertorque than men (see Fig. 12). A fraction of the energycost of swimming is utilized to overcome the torque to keepthe body in the horizontal position, the most favorable forobvious reasons. Because of their structure, men are obligedto spend more energy to this aim, hence a greater energycost of swimming. In fact, this last is linearly related to theunderwater torque (T) (Fig. 12), the function CIT in swim-mers of similar skill being essentially the same for bothsexes (55). In addition, even within the same sex, the inter-individual variations of torque are rather large, thus contri-buting to increase the interindividual variability of C. In-deed, the coefficient of variation of C attains 27% and 30%in noncompetitive men and women, respectively. In collegeswimmers, the coefficient of variation of C is less, amountingto about 15%, a fact that reflects presumably a more uni-form technique andlor smaller interindividual variations oftorque. In conclusion, because of purely anthropometricreasons, women swim more economically than men. Thefollowing considerations can be drawn from this state ofaffairs:

60

m102 rn'rn2

t2

C

kJ•m'm1

0.9

0.6

0.6 1.0 Il. 1.8 2.2m.s

20

1.5

(mIOz)

l.0

40

0.5I I I 20

0.4 0.8 1.2

Fig. 11 Energy cost above resting of swimming different strokes inelite male swimmers (kJ m' or ml °2 m). 0 = crawl; V = back-stroke; o = breaststroke; = dolphin. From Holmér (33).

_-0.

that poor swimmers are less so when swimming the breast-

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66 mt. J. Sports Med. 7 (1986) P.E. di Prampero

I I I

0 10 20 30

T (N ml

Fig. 12 Energy cost above resting of swimming the crawl, kJ mand per m2 of body surface, as a function of the underwater torque(T, N m) in men (o) and women (.) of low technical skill. Averagevalues of energy cost were 0.88 0.24 and 0.63 0.19 kJ m ' (± SD)per m2 body surface, in men and women, respectively. Upper part offigure is a schematic representation of the method used for assessingunderwater torque. The subject lies on a rigid beam free to rotatearound an axle (RI which coincides with the center of air of the lungs.The underwater weight at the feet level is determined by a straingauge (P). The product of the distance, R-feet, times the force, P,yields the underwater torque. Data from Pendergast et al. (55).

1. The anthropometric characteristics that underly the dif-ferences of C establish themselves at puberty, beforewhich C is the same in boys and girls (Pendergast, D.R.,personal communication). Thus, other things being equal,boys can be expected to "deteriorate" their performanceafter puberty.

2. A type of training that leads to a large increase of theleg muscles may be negative in terms of performancesince, via its effects on T, it may lead to an increase ofC. In quantitative terms, leg muscle training becomesnegative when the increase of max which it produces isless than the concomitant increase of C, so that the ratioEmax/C becomes smaller. While this is theoretically verystraightforward, it becomes very difficult, if not impos.sible, to propose general rules thereabout.

3. A similar type of analysis as applied here to women andmen may explain the well known fact that, generallyspeaking, blacks are poor swimmers. In fact, the overallweight of the skeleton and the density of the lean bodymass are 1O%—20% and 1%, respectively, larger in theblack than in the white population of North America(52, 63, 64). This can be expected to lead, ceteris pan-bus, to higher T values and hence to poorer swimmingperformances in the blacks. It goes without saying thatthis anthropometric factor does coexist with the socio-economical ones usually invoked to explain the lesserswimming performances of the blacks.

5.1.3 Drag and EfficiencyDuring constant speed swimming, the greatest fraction ofthe energy expenditure is utilized to overcome water re-sistance, or drag (D). This is so because the speed fluc-tuations at each stroke are small (especially for the frontcrawl), and essentially no energy is used against gravity orair resistance. Thus, the external power output (we) can beviewed as the product of D times the speed relative to thewater (v):

'e=Dv (12)Neglecting the possible occurrence of internal work, the over-all mechanical efficiency (??)of swimming is then given by:

??/eE'DvE1 (13)It thus becomes apparent that the assessment of D is anecessary prerequisite for the calculation of??.

Several authors have determined D on subjects passivelytowed in water (35, 37, 44). However, during actual swim-ming, because of the movements of the arms, legs, andhead, and of the changes of buoyancy due to breathing, Dis greater than for passively towed swimmers.

In actual swimming conditions, D can be assessed by anindirect method, as follows (25). The body drag of subjectsswimming at constant speed is increased, or decreased, bya known amount (added drag, DA), applying to the swim-mers' body known forces acting along the direction ofmovement (Fig. 13). Under these conditions, the relation-ship between steady state 02 consumption and added drag(DA) is linear for a given speed. Extrapolation of the V02 IDA relationship to resting V02 yields on the x axis theforce which, applied to the swimmer in the forward direc-tion, would propel him at the given speed without any in-crease of energy requirement above resting. This force istherefore equal in absolute terms, and opposite in sign, tothe average drag the subject has to overcome at that speed.

This line of reasoning seems rather intuitive; it can, however,be derived formally as follows. The steady state 02 con-sumption above resting (V02 S) is linearly related to the totaldrag (DT) to be overcome by the subject (see Fig. 13).

025=aDT (14)DT is the sum of the drag due to the swimmers' body (D),constant for a given speed, plus the added drag, DA:

DT=D+DA (15)Substituting Eq. 15 into Eq. 14, setting j02S 0, rear-ranging, and solving for D, one obtains

D=—DA0 (16)where DA0 is the added drag obtained by extrapolation ofthe V02 5/DA function to V025 = 0.

In addition, this method dso allows calculation of the energyrequirement for swimming at speeds greater than that corre-sponding to the subject's VO2max. In this case, the V02/DArelationship is determined in the range of the negative DAvalues which allow an aerobic steady state to be attained.The function is then extrapolated to DA = 0, to obtain the°2 requirement to swim at the given speed without theaid of supplementary added forces (Fig. 13).

01.5

kJ m1m2

1

0.5

000 /•00,0 '0 •,00.,o.,

o: M•: F

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L1f

/

-120 -50 -40 0 -10-

0 0

DAIN) DAIN)

Fig. 13 Oxygen consumption above resting (''O2, I mm') whenswimming the crawl at constant speed (1.7, or 0.4 m ) as afunction of the added drag IDA, N). Upper panels show schematical-ly the method used to apply known DA values to the swimmer'sbody. Note that the platform moves at the same speed of the swim-mer. The body drag of the swimmer at speed v is obtained by extra-polating the function VO IDA to V02 =0. When the speed is greaterthan that corresponding to the subject's Va2 max, the extrapolationof the function to DA = 0 is a measure, in 02 equivalents, of theenergy requirement to swim at the given speed, without the help ofany externally added forces. See text for details. From di Pramperoet al. (25).

The results of D and t obtained with the aid of this methodon six college swimmers are indicated in Fig. 14 from un-published observations by di Prampero and Pendergast.These values are about twice larger than those obtained,by passive towing methods, a fact which underlines the im-portance of the limbs, head, and respiratory movements indetermining the drag during actual swimming. D increaseswith the speed as described by:

D=58v1-2 (17)where D is in N and v in m s.When swimming on the surface, the overall drag is the re-sult of: (1) friction drag, which depends on the type andsize of the wetted surface; (2) surface drag, which dependson the size and shape of the body; and (3) wave formation.

The exponent of Eq. 17 depends on: (a) the three individ-ual functions relating the above drag components to thespeed and (b) their relative importance, at any given speed,in setting the overall D. The data available at present donot permit one to disentangle the above factors from eachother.

The efficiency values reported in Fig. 14 for swimming arelower than in most forms of human locomotion, a fact thatis responsible, together with the large water resistance, forthe great energy cost of swimming. The use of fins to increasethe propelling action of the lower limbs allows attainmentof swimming efficiencies on the order of 15% (di Pramperoand Pendergast, unpublished observations), not far fromthose obtained on trouts swimming at cruising speeds (74).

5.2 RowingThe most economical form of water locomotion is rowing,partly because of the use of a propelling system with arelatively high efficiency and partly because of the choiceof proper shapes and sizes of the shell, reducing water dragto minimal values. The paragraphs that follow are devotedto a brief analysis of the biomechanics and bioenergetics ofrowing.

5.2.1 Mechanical WorkThe external mechanical work (we) performed by the rowerto travel the distance s during the time t is given by:

we= / FpdS7 Fpdt (18)

where Fp is the propulsive force exerted by the rower andthe average speed of the boat. Neglecting the work ab-

sorbed by the deformations of the shell and oars, as well asthe air resistance, the work done per unit distance is en-tirely dissipated against the water resistance. Hence:

Db = - = 0.7 V J' Fp dt (19)

where Db is the average drag of the boat over the distance s.The factor 0.7 has to be introduced since, because of theretrograde movement of the oar blade in water, only about70% of we is actually utilized to propel the boat (2, 10).

Db has been calculated according to Eq. 19, measuring Fpby means of strain gauges applied on the oarlock pin (10).For a standard two oars shell with coxwain, Db was found toincrease approximately with the square of the average speed(i):

Db=4.795 (20)

E —,

mO, 4voi—

.

/S •

V. l?ms V. 0.40,,,s'

0

120

0(N)

80

40

V02 1/mm 3

I -, _0

.8

-p.-

0.12

006

0.04

_o_ — — — _°:.--t2 1.8 ms' 2.C

Fig. 14 Water drag ID) and efficiency of progression () as afunction of the speed when swimming the crawl (college swim-mers, Pendergast et al. (55)1 and in kayaking. Data for kayakingwere obtained with the same method described in Fig. 13 (Cerre-tell) and Pendergast, personal communication, 1984).

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where Db is inN and V in m s'. Hence, the external mech-anical power, we, is given by:

= Db V = 4.7 V 2.95

where, for V in m s' , 'e is in W.

It must be pointed out that the values of Db calculated ac-cording to Eq. 19 are larger than those obtained by towingthe shell + crew. During actual rowing, in fact, because ofthe pulsatile propelling action of the oars, the speed oscil-lates in an approximate sinusoidal fashion around the mean.As a consequence, and since Db increases with the squareof the speed (Eq. 20), the average resistance encounteredby the shell at a given average speed is larger than it wouldbe were the speed constant.

5.2.2 Energy Cost and EfficiencyThe energy cost of rowing, as determined by di Pramperoet al. (22), is indicated in Fig. 15 as a function of the speed.The values refer to one oarsman on a two oars shell with cox-wain; as a consequence, the overall energy cost of transportof the shell is twice that reported in Fig. 15. These dataare to be compared with those observed in kayaking whichattain 0.4 kJ m1 at a speed of 2.3 m s1 and in swim-ming the front crawl which attain 1.0 kJ m at a speedof -'l.O m s' in swimmers of good technical skill. Thus,rowing seems to be the most economical form of aquaticlocomotion, at least as far as racing shells are concerned.

The data reported in Fig. 15 allow calculation of the over-all efficiency of progression during rowing (22): it increaseswith the speed from -0.1 at 3 m s' to 'O.16 at 4.5 m sThese values of efficiency take into account the fact that onlyabout 70% of the work done by the rower is wasted becauseof the retrograde movement of the oar blade in water. Thus,the actual efficiency of work performance by the oarsmenis about 40% larger (22, 29, 30).

5.2.3 Stroke Frequency and Economy of ProgressionBecause of the pulsatile action of the oars, the mass of theshell + crew is accelerated during the pull phase; at constantspeed, an equal deceleration takes place in the recoveryphase of the stroke. This leads to speed fluctuations aroundthe mean, which are damped, to a certain extent, by themovements of the oarsmen in respect to the shell. In fact,during the pull phase of the stroke, the oarsmen bodiesmove forward and during the recovery phase they movebackward, thus acting as a flywheel. In spite of this intrin-sic mechanism, the speed oscillations are not abolished.They are a decreasing function of the rowing frequency; ina speed range between 3 and 4.2 m they amount to15% of the mean speed at 0.35 Hz and to only 4% at 0.62Hz (10).Since the water resistance increases with the square of thespeed (see Eq. 20) at a given mean speed, the average dragof the shell is larger with greater speed oscillations. Hence,ceteris paribus, the progression is more economical thehigher the rowing frequency.High frequencies are more economical for yet anotherreason. Because of the geometry of the system, the pullphase of the stroke generates a transverse force (10) whichis obviously useless in terms of progression as it tends only

(21) to deform the shell. The transverse force is proportional tothe cosine of the angle between the oar and the directionof movement, being zero when the oar is at right angle withit (cos 90° = 0). Since, at a given speed, the angle coveredby the oar during the pull phase is smaller the higher thefrequency, it necessarily follows that high frequencies areaccompanied by a lesser waste of energy.

It can be concluded that, other things being equal, the pro-gression is more economical at higher frequencies. Obvious-ly enough, the upper limit to this state of affairs is set bythe frequency above which the speed of muscle shorteningis so high as to lead to a decrease of the efficiency of con-traction.

6 Energetic Analysis of World Records

World records* constitute an extremely interesting collec-tion of data: (1) because of their accuracy which far ex-ceeds that of the best laboratory measurements and (2) be-cause they constitute the upper limit of human perfor-mance at a given time in history; hence the interest ofhuman physiologists for world records (47, 53, 54, 60).A quick inspection of Eq. 2:

vT = Emax c_i (2)

0.24

0.20

0.16

0.4

0.3

//7E

0

0.05

2.5 3.5 4.5ms

Fig. 15 Water drag (Db), energy cost (C), and efficiency (s) as afunction of the speed for one rower on a two oars racing shell withcoxwain. The energy cost and drag for the overall shell are there-fore twice as reported here. Data from di Prampero et al. (22) andCelentano et al. (10).

* Strictly speaking, the term "record" defines the best performanceto date in a given event in standardized conditions concerning, e.g.,wind speed and type of track. In several forms of locomotion, suchas skating, rowing, or the marathon, such a standardization has notbeen made. In these cases, it is more appropriate to speak of "bestperformances," rather than records, a distinction which will beneglected here.

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shows that a top performance is the result of the appropriatecombination of two ingredients: the subject's maximal mus-cular power (Emax) and the energy cost of locomotion (C).

The aim of the section that follows is to calculate the theo-retical max values in running, skating, and swimming byinserting into Eq. 2 the appropriate C values discussed else-where in this article and assigning to Emax a value appli-cable to elite athletes. The thus obtained theoretical valuesfor max will be compared with actual record speeds toshow that theoretical and actual speeds are rather close.

The maximal mechanical power a given subject can main-tain at a constant level throughout the effort is a decreas-ing function of the effort duration to exhaustion. Wilkie(75) has analyzed the relation between external power incycling (wemx) and duration of the exercise to exhaustionbetween 40 s and 10 mm, longer durations having been ex-cluded because of the difficulty of assessing precisely theexhaustion time. According to Wilkie (75), the relationshipbetween wema( (kW) and exhaustion time (t, s) is describedby:

wemax = A t + B — Br(1 — &t/T) t1where A is the amount of mechanical work that can be de-rived from anaerobic (lactic and alactic) sources, B themechanical power sustainable on the basis of VO2max, andr = 10 s is the time constant of the kinetics of V02 at theonset of exercise. The third term of Eq. 22 reflects the factthat V02 max is not reached instantaneously at the onset ofwork: its weight is rather small and decreases with increasingt from 11% of wem at 40 s to 1.5% at 10 mm. Both A andB in Eq. 22 can vary depending on the athletic characteristicsof the subject; for Wilkie's subjects A = 16 kJ and B = 0.273kW.

On these bases, it seems reasonable to describe the relation-ship between maximal metabolic power (Emax) and ex-haustion time (t) in similar terms:

Emax=Eanft +MAP—MAP r(lettT)t1where Ean is the maximal amount on energy obtainable byanaerobic (alactic and lactic) sources, MAP the subject'smaximal metabolic aerobic power, and r has the same mean-ing and the same value ( 10 s) as in Eq. 22. If this is so,Emax can be calculated for any given value of the exhaustiontime (t) assigning to Ean and MAP the values applicable toelite athletes. This has been done in Fig. 16 assuming, fora 70-kg, 175-cm athlete MAP = 1.8 kW (74 ml 02 kg' miiiabove resting) and Ean 100 kJ (68 ml 02 kg), this lastbeing the amount of energy released by complete exploita-tion of alactic and lactic sources (20).

The maximal speed can now be obtained as a function ofthe exhaustion time, inserting Eq. 23 into Eq. 2, and pro-vided that C is known:

max = C1 [Ean t + MAP — MAP r (1- etfr)t1 1 (24)

It has been shown on theoretical grounds (38) that to estab-lish a maximal performance in a given event: (1) the poweroutput must be constant throughout the event and maximalgiven the duration of effort, this obviously implying that(2) the time of performance must coincide with the exhaus-tion time. On these bases, therefore, when setting into Eq.24 t equal to a given record time, the resulting max should

Fig. 16 Upper panel shows the maximal external power (kW) thata well-trained nonathletic subject can maintain at a constant levelduring cycloergometric exercise, as a function of the effort durationto exhaustion. Data from Wilkie (75). On the basis of Wilkie's

(22) analysis, the relationship between maximal metabolic power (kW)and effort duration to exhaustion has been given the same generalform for an athletic subject (middle panel). In the lower panel, themaximal power has been partitioned into aerobic and anaerobic(alactic + lactic) components. Thin continuous line shows behaviorof aerobic vs anaerobic partition were VO max instantaneouslyattained at the onset of exercise. See text for details and mathema-tical analysis of curves.

be equal to the corresponding record speed. The thus calcu-lated max values have been compared with the actual recordspeeds for the 400 to 10,000 m in running, 1000 to 10,000m in ice-speed-skating, and 100 to 1500 m in swimming.Shorter performances have been neglected since the timerequired for full exploitation of the anaerobic (lactic + alac-tic) sources is > 40 s (20). Longer perfomances have also

(23)been neglected since VO2 max cannot be sustained indefi-nitely. The values of C assumed in the calculations are thosereported in Table 2 for running and skating and in Fig. 10for elite swimmers. The values for swimming have been redu-ced by 10%, to take into account the initial dive and the pushon the wall of the pool at each 50-rn stretch during competi-tive swimming. Both these factors, in fact, reduce the energycost of swimming as compared with the values reported inFig. 10, which were obtained in a swimming flume.

For running and speed-skating, C has been corrected totake into account the initial acceleration. The energy spentin this phase was calculated as 0.5 M V2 1 where M isthe mass of the subject, V the average record speed, and ithe efficiency of transformation of metabolic into kineticenergy. Thus, in running and skating, C can be described as:

C = CNA + k' V2 + 0.5 MV2 n (25)where CNA and k' are the values reported in Table 2 fora 70-kg, 175-cm man, V is the actual speed of the record(m s'), d the distance covered (m), M = 70kg, and

= 0.25. It has been assumed that i = 0.25 since in theinitial acceleration phase no recovery of elastic energy cantake place (9) and hence the overall efficiency of exercisemust approach the efficiency of muscular contraction.The third term of Eq. 25 plays an appreciable role in the

E too

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Table 8 World records (men) and corresponding speeds in the indicated events. The energy cost above resting for a 70-kg, 175-cm man at therecord speed is also indicated. Predicted speed was calculated from the maximal metabolic power that a typical elite athlete can sustain over thetime in question (Emax) and the reported value of C, as from Eq. 24. Percentage difference between predicted and record speeds is also indi-cated. See text for details.

shortest distances, accounting for 8% and 11% of C in the400 m and 1000 m in running and skating, respectively. Forlonger distances, it decreases progressively to attain 0.2%and 1% for the 10,000 m in running and skating.

The results of such calculations are reported in Table 8,which shows that: (I) for running, with the exception ofthe 400 m, the agreement between predicted and actualspeed is excellent and (2) for skating and swimming, pre-dicted underestimated observed values by 9.8% on theaverage.

As far as the 400m running event is concerned, the over-estimate can be due to the fact that: (1) the record time istoo short to allow for full utilization of the anaerobic alacticand lactic sources in athletes and/or (2) the assumed VO2maxof 75 ml kg1 • min1 above resting is too high for a sprinter.In fact, the VO2max of P. Mennea, the actual recordman ofthe 200 m (19.72 s), at the time of his top performancewas 59 ml kg'' min1 above resting (A. Dal Monte, per-sonal communication, 1985). If this value is inserted intoEq. 25, the predicted speed turns out to be 9.46 m s, i.e.,only about 4% above the actual record speed.

In skating, predicted underestimated observed speeds from—7.3% to —12.8%. This finding may be due to the factthat the values of CNA and of k' for skating reported inTable 2 and used in the calculations were obtained onItalian skaters of good national level, but rather far fromworld class performances. Thus, their technique may havebeen somewhat inferior as compared with elite skaters.

In swimming, predicted underestimated observed valuesfrom —5.5% to —10.3%, indicating either that the value ofC used in the calculation is too high and/or that the VO2maxvalues of elite swimmers is larger than assumed here.

It should also be pointed out that Eq. 25 represents theenergetic bottleneck of maximal performances. Indeed, an

athlete who on theoretical grounds has the possibility ofestablishing a record may not be in the position to exploithis potential in actual practice because of the superveningof other (e.g., psychological) contrary effects.

In spite of the discrepancies discussed above, the agree-ment between facts and theories is rather good and couldpresumably be further improved by utilizing in the calcu-lations the individual values of Emax and C rather than theaverages as was here necessarily the case. This seems to pro-vide sound proof that our knowledge of the energetics ofmuscular exercise, on the one side, and of human locomo-tion, on the other, are satisfactory.

7 Summary and Conclusions

The energy cost of the forms of locomotion discussedthroughout this article is summarized in Table 9.This table, as well as the preceding sections of this article,are designed to provide a rather comprehensive and simpleset of information for potential readers: medical doctors,who should be able to prescribe to their patients (obese,hypertensive, cardiac, etc.) the correct amount and type ofexercise, thus making use of exercise as of any other drug,of which it is imperative to know posology and contra-indications; athletes, trainers, and sportsmen in general,who should gear correctly their diet to the type and amountof physical exercise; physical educators, who should beaware of the specific characteristics of the exercise modesthey propose to their pupils, as a function of their sex,age, and athletic capacity,

However, besides these practical applications, the notionsdiscussed throughout this article bear also a more generalinterest. Indeed, they allow a better understanding of themotion of man, that is, of the only machine, which besidesmoving about, also tries to understand how he does it.

Distance Record Record C Emaxtime speed

(km) (s) (ms1) (kJ ' km') (kW)

Running

Skating

Swimming

Predicted Errorspeed

(m's'J (%)

0.4 43.86 9.120 0.359 3.675 10.24 + 12.30.8 101.73 7.864 0.325 2.606 8.01 + 1.91.0 132.18 7.565 0.319 2.420 7.58 + 0.21.5 209.45 7.162 0.311 2.189 7.06 — 1.45.0 780.40 6.407 0.301 1.905 6.33 — 1.2

10.0 1633.81 6.121 0.298 1.850 6.22 + 1.6

1.0 73.60 13.587 0.242 2.914 12.06 — 11.31.5 114.79 13067 0.221 2.514 11.39 — 12.83.0 244.06 12.292 0.196 2.136 10.88 — 11.55.0 416.91 11.993 0.188 1.997 10.64 — 11.3

10.0 866.70 11.538 0.177 1.895 10.70 — 7.3

0.1 48.95 2.043 2.00 3.464 1.93 — 5.50.2 107.44 1.862 1.70 2.557 1.67 — 1030.4 227.80 1.756 1.50 2.159 1.60 — 8.91.5 894.56 1.677 1.38 1.892 1.52 — 9.4

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Table 9 Energy cost above resting (J m) in different forms of locomotion for a 70-kg, 175-cm man at sea level, on flat uniform terrain (whenapplicable) in the absence of wind or water current. v = speed (m s); F = snow friction of the skis. Further details and references are to befound at the sections indicated.

C(J' m)

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Locomotion Notes Section

Natural walking 140 At the optimal speed(-1.2m-s) 4.1

Competitive walking 100 + 64 v + 0.83 v2 v> 2 ' s_I 4.1

Running 270 + 0.72v2 — 4.1

Ice-speed-skating 70 + 0.79 v2 Good skaters in "dropped posture" 4.1

Cycling 13 + 0.77 v2 Conventional racing bike, "dropped posture" 4.1

Cross-country skiing 38 + 33F + 28 v2 "Double pole" 4.2

Swimming the crawl 1000 0.5 <v < 1.0Men, medium high skill 5.1

Rowing 19 v2 v > 3.7, for one oarsmen on atwo oars shell with coxwain 5.2

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P.E. diPrampero, Dèpartement de Physiologie, C.M. U., 1, rue Michel-Servet, CH-1211 Genève 4 (Switzerland)

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