Modern Engineering Thermodynamics

714 CHAPTER 17: Thermodynamics of Biological Systems
17.8 LOCOMOTION TRANSPORT NUMBER
Air, water, and land constitute the three common transport media available on Earth. Accordingly, we assign the
following locomotion mechanisms to these media: air, flying; water, swimming; and land, crawling and running.
An effective way to study the energy consumption of locomotion is through the dimensionless locomotion
transport number T, defined as
T =
P
(17.22)
wV
where P is the animal’s total rate of energy (power) expenditure during locomotion (often determined by
measuring the rate of O 2 consumption during locomotion), w is the animal’s weight(notmass),andV is its
locomotion velocity. At zero velocity, P = P o (the BMR) and T becomes infinite. The most efficient transport
velocity is the velocity for which T is a minimum. If we ignore aerodynamic drag and assume that P is independent
of V, thenT ! 0asV ! ∞. The faster the animal moves, the more efficient is its locomotion. This,
clearly, is unrealistic, since aerodynamic drag becomes important at even moderate speeds and inertia also
becomes important because the animal increases its velocity by flexing its locomotion muscles (legs, wings,
etc.) faster. Therefore P cannot be independent of V.
We can represent total power expenditure during locomotion, P, as
P = P o + P D + P m
HOW EFFECTIVE IS WALKING?
When you walk, some of the kinetic energy of your forward motion
is converted into potential energy as you rise on one foot, and a portion
of this potential energy is converted back into kinetic energy
again as you push forward and drop onto the other foot (Figure
17.11). The efficiency of slow walking is such that only about 65%
of your body’s kinetic energy is carried forward from one step to
another. Internal friction and other irreversibilities in your body consume
the remaining 35%. To keep moving, the lost kinetic energy
must be replaced by flexing the muscles in your legs, and this energy
ultimately comes from the food you eat.
When you get tired walking, you have used up your leg muscles’
energy reserve and your body cannot produce it from the stored
body fat as fast as it is needed by the muscles. Also, when you carry
a load in your arms or on your back when you walk, more energy is
lost through increased friction (though the percentage of body plus
load kinetic energy lost is about the same). However, African women
have somehow learned how to carry loads of up to one fifth of their
body weight in baskets on their head without using any additional
energy in slow walking.
Since 35% of the kinetic energy is 0.35(mV 2 /2g c ) = 0.175(mV 2 /g c ), and
muscle efficiency is only about 25%, then the total energy consumed
in slow walking is about 4(0.175)(mV 2 /g c )=0.7(mV 2 /g c ). For a 180.
lbm person walking at 3.00 ft/s, the energy requirement per step in
slow walking is
0:7ð180:lbmÞð3:00 ft/sÞ 2 /32:2 lbm:ft/lbf .s 2 = 35:2ft× lbf/step
FIGURE 17.11
Person walking.
and, if the walker has a velocity of 2.00 steps/s, then the energy
rate is
ð35:2ft.lbf/stepÞð2:00 steps/sÞ = 70:4ft:lbf/s × 1 Btu/778 ft.lbf = 0:0905 Btu/s
Now, 1 Btu = 1.055 kJ, so the energy rate needed is 0.0905 × 1.055 = 0.0955 kJ/s, or 0.0955 kJ/s × (3600 s/h) = 344 kJ/h =
0.344 MJ/h. Table 17.5 lists “fast” walking as requiring 1.3 MJ/h. Since the basal metabolic rate is 0.3 MJ/h, then the fast
walking alone is 1.0 MJ/h, which is about three times the slow walking rate just calculated.