Environmental Engineering Reference
In-Depth Information
contacting the ground), and Froude numbers (dimen-
sionless Fr
¼
v
2
=
gh, where h is a characteristic length,
such as hip height). Run is a gait with duty factor
<
0.5,
and changes from walk to trot take place when Fr
¼
0
:
3-
0.5 and from trot to gallop when Fr
¼
2-3. There is no
substantial difference between the COT of bipedal and
quadrupedal running of animals who can do both (mon-
keys), nor between the bipedal running of birds and the
quadrupedal motion of mammals. The number of steps a
running animal must take per unit of distance will be
inversely proportional to its length (roughly to M
0
:
33
),
and the work accomplished for each step must be pro-
portional to its mass.
Net metabolic COT thus scales as M
0
:
33
; when run-
ning faster, the smaller creatures must take many more
steps, each one needing power in direct proportion to its
M (fig. 4.7). At the same time, all running animals have
to deal with the same biomechanical constraints, and
hence their mechanical COT (distinct from metabolic
COT) is independent of mass. A 10-g lizard will have a
metabolic COT 1 OM higher than a 100-kg mammal,
but their mechanical COTs will be very similar, at about
1J/kg
m (Alexander 2005). Maximum oxygen con-
sumption increases with M
0
:
85
, whereas the exponent
for the total running costs is only 0.67. Because the avail-
able power goes up faster than the cost of running, large
mammals (bears, hippos, buffaloes) are able to run much
faster (up to ten times) than the smallest ones. Large
mammals also save much energy in running because of
the elastic structure of their legs. Kinetic or potential
energy lost at one stage of the stride is temporarily stored
as elastic strain in both muscles and tendons, to be used
later as elastic recoil (Alexander 1984).
At high speeds some mammals, including humans,
may save more than half the metabolic energy they
would otherwise need in running. Similarly, penguin
waddling conserves mechanical energy, and its high COT
is due to the animal's short legs, which require rapid
generation of muscular force (Griffin and Kram 2000).
Cheetahs are the fastest runners, reliably measured at
105 km/h, or 29.1 m/s (Sharp 1997), but like other
sprinters they cannot sustain speed for more than a few
100 m. Eaton's (1974) records show 60-90 m as the
usual rushing distance, and during successful hunts the
distance between cheetahs and the prey when it started
to run was merely 45 m. The high energy cost of these
rushes (up to 156 breaths/min after a dash and kill com-
pared to 16 breaths/min at rest) requires subsequent
recovery and limits the number of such intensive chases.
In contrast, fast-moving elephants are not really run-
ning (Hutchinson et al. 2003). Although their duty
factors are as low as 0.37 and their Fr values could
surpass 3.0 (both far above quadrupedal walking gait),
they always keep at least one foot in contact with the
ground.
Jumping has a counterintuitive limit: energy output is
directly proportional to the muscle mass, which is gener-
ally proportional to the total body mass; identical energy
release per unit mass should then raise the animals to
equal heights. This expectation is confirmed by measure-
ments for animals whose body sizes differ more than
10
8
-fold. A flea (0.49 mg) jumps 20 cm, a locust (3 g)
60 cm, and a human (70 kg) 60 cm (this refers to the
lifting of the body center during a standing jump that
does not utilize the kinetic energy of high jumping). Be-
cause air resistance is very important for tiny insects, the
threefold difference between a flea and a person would
virtually disappear in a vacuum. African bush babies (Gal-
ago) jump up to 2.25 m, but their jumping muscles
are about twice as massive as in humans. Distance, not
