11: Caloric Costs of Mass Transport Henry A. Bent Norlh Carolina State University
Raleigh, 27650
runner would. In addition to doing work against gravitv, however, real runners expend energy againstinertia, accei: erating and decelerating arms and legs during each stride. Qualitatively, if not- fully quant%atively, however, the simple, stiff-leg model of locomotion accounts for the small stride-leneths of heavilv loaded backoackers., old neoole. and tired walkers; the smooth gait of experienced distance runners, compared to the bounding action of sprinters; the gravity in distance running of over-striding; and the relatively high runnine efficiencies of laree .. auadruneds. . Large dogs and horses trotting 8 mph take relatively short, raoid strides. Gerbils. mice. and other small ouadruneds. . , on thk other hand, whenthey do run must run nearly flat-out, if only for short distances, and have large specific energy expenditures. In running wheels gerbils train more like sprinters than distance runners, executing repeatedly brief bouts of brisk running followed by approximately equal intervals of rest. The stiff-leg, work-against-gravity model of locomotion helps to account, also, for the nearly direct proportionality
The greater one's running rate the greater one's energy expenditure rate-hut the farther one goes. Run fast or slow, 10 mph or 8 mph, the caloric cost of covering one mile is, interestingly, about the same (Box 5): 120 kcal/mile- for a 70 kg person. For a 140 kg person-or for a 70 kg person carrying a 70 kg load-the caloric cost of mass transport is about twice as great. In SI units. the cost (in Joules: 4.184 J = 1cal = 4.184 ke" m2 s - ~ )of transporting by running a unit mass (1 kilogram) a unit distance (1 meter; 1609 m = 1mile) is about 4.9 120 kcallmile x- 4184 J -J = 4,9 m 1mile - 4,9 70 ke "
1 kcal
lfiO9m
kern 0
. . .
-
a2
For comparison, the acceleration due to gravity,g, is at sea level 9.8 m/s2. g may be viewed as the energy required to raise a unit mass a unit distance
I n summary, the caloric cost of transporting a mass horizontally, by running or jogging, is (not coincidentally, see next section) of the same order of magnitude as the caloric cost of transporting the same mass the same distance vertically. Stlff-Leg Model of Locomotlon Jogging is described in dictionaries as "moving up and down." Running and walking are a series of forward falls followed by recoveries. During recovery phases, work is done against gravity. Running is a battle up hills. During jogging's uphill battles, energy expended will depend on the force of gravity (running on the moon is easier than running on the same surface with the same load on the earth) and on the ouantitv of mass elevated. Partlv for that reason world-class distance runners are usually light-boned thin ectomorphs running %7% fat compared to 1620% fat for average adult US. males. Many marathoners are, by insurance comoanv mara. . tables. 20-30 lh "underweieht." - . althoueh " thoniug senior citizens appear to he excellent life-insurance risks. For strirtly stiff-legged striders, an appliration of Pytharoras's theorem (Hox 6 ) shows that the shurter the strider's itrides the leas the work done against gravity per unit distance travelled (Box 7, last column). As indicated at the bottom of Box 7, the stiff-leg model of locomotion amears t o account for the entire caloric cost of running. In f k t , real runners hend their knees and, thereby, bob up and down about one-third as much a i a stlff-legged Box 5. Caloric Costs of Human Activities
1
Box 6. Stiff-Leg Model of Locomotion L =Leg Length S = Stride Length (Foot-lens% ignored)
I
Box 7. LeglStride Ratios and Work Against Gravity Nature Of Stride
C
[C -
Leg Length. L
S
S
2.0 1.5 10 0.5
0.50 0.67 1.0
Stri*
Length, S
(See Box 6)
70 kg person .iving 2400 kcal = 100 kcat = 1.67
w
F
E= 0.16 hp mtn
Flat-Out Long Normal Short
Sleeping 1 Standing 2 Walkin 4 3m& Running 6 mph 16 X (60 minla mlles) X (60 minIl0 miles) 10 mph 20 :or Mm"B.iSOB--.-. -. ne sllce of bread metabolized u 80 kcai u 1 mile walked One lb adipose tissue metabolized a 3500 kcai = 44 mlles walked
I 526 1 Journal of Chemical EducaNon
dm]
I I
2.0
0.50 g 0.23 g 0.13 g 0.06 g
For a normal still stride. (Chemical Energy Input)
= (Potential Energy increment) Chem. C,input Mech. E. Output
between energy-expended-per-mile and the quantity of mass transported and for the high efficienciesof locomotion of both swimming fish and bicycling humans, who do little work against gravity. Bicycling Bicycles are remarkable vehicles. Between 35 and 40 million are produced worldwide per year. In most parts of the world they play amore useful role than automobiles. In addition to providing reliable transportation, they make a positive contribution to cyclists' health; they contribute little to air and noise pollution and (of themselves) to traffic deaths; they require simple pathways, little parking space, no filling s,tations; and they make little demand on the world's mineral and fossil fuel reserves. Modern light-weight bicycles weigh about 30 lh and can transport ten times their own weight, a figure not approached by any bridge, automobile, or aircraft. And a t normal operating speeds, a steady-seated cyclist-the ultimate in jointbending, non-bobbing locomotion-is No. 1among all moving creatures and machines in efficiency, energy consumption per distance travelled being approximately only one-fifth that for running, (Box 8). Running 10 mph, for example, requires a metabolic input of about 20 kcallmin (Box 5). bicycling only about 4 k c d m i n (Box 8, column IV)-or, per hour, 240 kcal(2 hot dogs, 2 soft rolls, or 2 large bananas); and, per 100 miles, 2400 kcal (a normal person's daily caloric requirement). Power outputs calculated to he necessary to overcome air resistance and rolling resistance (column 11) and maximum power outputs estimated (column V) from measured oxygen consumption rates (column 111) are, as they should be, approximately equal. Power outputs expressed in horsepower (column 11) are approximately froth oxygen consumption rates expressed in liters per minute (column 111). T o maintain on a touring hicycle a speed of, for example, 30 mph (about the maximum speed of a "moped") would require (column 11) a power output of about 1.3 hp (about the hp-rating of a moped's engine) and an 0%-consumptionrate of about 1.3 X 10 = 13 Ilmin, over twice what humans can achieve. The maximum speed trained cyclists can maintain for several hours is about 25 mph. That speed corresponds to a power output of about 0.4 hp (Box 8, columns IA and 11; also Box 2 Part I, July issue, p. 000) and to a metabolic input of about 20 kcallmin (column IV) or, per 100 miles travelled (in 4 hours), to 20 X 60 X 4 = 4800 kcal, over twice the input required if cycling 100 miles a t 10 mph. Haste makes wasteand heat. In competitive 24-hour rides champion cyclists maintain speeds near 22 mph and metabolic inputs of about 15 kcall min, creating in 24 hours a caloric deficit of about 15 X 60 X 24 20,000 kcal and a craving for food not satisfied until after several days of heavy eating.
-
In stationary, treadmill-like tests trained cyclists can maintain over long periods (about four hours) power outputs of only 0.2 hp, significantly less than the 0.3-0.4 hp outputs cited above for 24-hour and 100-miletrack and road races. The difference has been attributed to the cooling effect of the 22-25 mph wind created by a racing cyclist's motion. A cyclist racing 25 mph has, as noted, a total metabolic rate of about 20 kcallmin, a power output of about 0.4 hp, or 4 kcallmin, and, therefore, by the conservation of energy, a heat production rate of about 20 - 4 = 16 kcallmin. In the absence of any energy-removal mechanism, the temperature of a 70-kg cyclist (calorically equivalent to approximately 60 kg of water, which, in turn, is equivalent to 60 kcal of energy per degree C change in temperature) would rise about 16°C per hour kcal
16-X-
rnm
60 min 1hr
1°C in 60 kg HzO 60 kcal X
60 kg Hz0
= 16°C
in 1 cyclist
Voluntary exercise, and involuntary shivering, is a fast way to warm up. Indeed, in hot humid weather waste heat from prolonged vigorous exercise may produce heat prostration. Sweating A hot, head wind, however brisk, cannot chill a body purely by convection. As a Charles Blagden noted in 1775, the human body has, however, agreat power to destroy heat, even in hot weather. bv evanoration of water. standing wit6 several friends in a room heated to 260'F in which eees were roasted hard in twentv minutes. a heef-steak rather o;er-done in thirty-three m i k t e s , yet their body temperatures remained at 98"F, Blagden noted that exhaled air "agreeably cooled our fingers . . . [and] pure water in an earthen vessel never came near the boiling point. . . [until] a small quantity of oil was dropped into it [forming a harrier to evaporationl, in consequence of which the water came a t lenith to boll very brisklif.A saturated solution of salt in a,ater put into the room," continues Hlaaden, '.was Found to heat more quickly, and to a higher degree, than pure water, prohably because it evaporated less. Perhaps no experiments hitherto made." concittdes Biagden. ..furnish more rimarkahle instancesof the coolinr effect of evaporation.. . lwhichl inust undoubtedly prove a powerful assistant in keeping theliving body properly cool, when exposed to great heats." T o remove solely by evaporation energy released in metabolism of a 2400 kcallday diet would require evaporation of approximately 4 1or 20 glasses of water per day 1000 kcal 1g HzO evap. X -= 4.1 1 H 2 0 evap. 2400 -X day 584 cal 1000 g H ~ O k The maximum sweatine rate of normal adults under normal conditions is about 2 h.Completely evaporated, that water-loss corresponds to an energy-removal rate of nearly 20 kcallmin
I (11 Calcu/atd
(1) Speed (mph)
(A) Rm ng 0 10.5 14.5 19 22 25 27
Notes
] (IK)
I
(0) Tourmg 0 8.3 12 16 18.5 21 22.5 (30)
Owen, Consumption (ilmin)
0 0.05 0.1 0.2 0.3 0.4
0.3 0.75 112 2.1 3 3.9 4.8
?&I
(1'4 Calculated Metabolic
Measured (111)
Required Power(hp) output
&Kin)
1.5 3.75 6.0 10.5 15 19.5 24
('4
Estimated Maximum Power output PP) 0.04 0.09 0.14 0.25 0.35 0.46 0.56
Frontal Area 0.33mZ.total weigM 77 kg. Are pressure 100 lb/pz Frontal Area 0.50 m2: total wei ht 83 k ' tire ressura 50 lblin
+%
Re "ired Power o: ~ 6 t a~l e s i s z n c ex ee8 ?oral Resistance = Air Resistance go ling Resistance Alr Resstance a Frontal Area X s p e d Rolling Resistpce = (C C2/ Tire P r e u r e ) X Told Weight 0.3 i ~ m i n= restmgrate; 4 b 11mm .-. maxmum o2- mnsumption rate
+
i ( them. E Input ) X & 1
(lV)
Mech. E Output
(a) I
Volume 55. Number 8, August 1978 / 527
Box 9.
Aqueous Bicarbonate lo Gaseous Carbon Dloxlde At physioiogical pH 7.4 mast dissolved carbon dioxlde Is present a3 bicarbonate, in the proportionsHCOa~:H&O3:CO2(aq):COs2~::4l20:1:384:5
(1)
HC03-(as)+ Hf(aq)
3H&03(aq)
water lost per hour) to need (20 kcal of heat produced per minute). C02 Removal In'addition to by-product heat-about 2400 kcal per normal day-arising from the oxidation of carbohydrates + 0%= COz + Hz0 + Heat -CHOH30 g 1mol 120 kcal the body must remove by-product COz, a t the rate of about 14 mmolelmin 1day 1molCOn m 2400 kcal X -= 14 mmale COzImin dav 24 X 60min 120 kcal 10-3 Venous blood normally loses in the lungs about 2 mmoles of COz/l, through the reactions (1)-(3) described in Box 9. A loss of 14 mmoles of COs per minute would require, therefore, a blood flow rate of 1412 = 7 Vmin and, if the heart has a stroke volume of 100 ml, 70 heart beatslmin beat
m
X -= 70 beatsImin 100 ml blood Again, Nature achieves a nice match between ability (heart beat rate) and need (COz removal rate). 1-X
mm
Suggested Reading
-
-
k hr X -= 19.5 kcallmin 60min 1000 Interestingly, 20 kcallmin is approximately the maximum energy-production rate trained athletes can maintain over a period of several hours. Nature nicely matches ability (2 1of X-
528 I Journal of Chemical Education
Aatrand, P., and R d s h l , K . , " T e x t h k ofWorkPh~iolok/."M~Graw-HillBook&., New York. 1970. Wilke, D.R., "Man as a Source ofMeehsnics1 Power."Er#onomio., 3.1 (1960). DWieS, C. T. M., "Human Power output in Exerciseof Short Duration in Relationto B d y Sizp and Composition: E~gonomica,I4 12j.246 (1971). Coelil1,D. L.,and F0x.E. I..,"Encrpties ofMarstho" Running," Medkine."dSciom. in Spans. I [21.81(1969). Schmidt-Nieisen. K., "How Animab Work." Cambridge University P m , New York,
1972.
Wilson, S. S.,"BicycleTechnology."Sci. Am., 228 l31.81 (1973). Whit,, R. R.,"A Noicon the Estimation of,heEnergy Expenditureolsport~gc~yclists." Ergonomics. 14, [81.419(1971).
