9.8 Basal Metabolic Rate
339
think of Eq. (9.15) as a straight-line approximation, near human adult masses, to a
full BMR function of mass.
The condition lim M→0 dQ/dt = 0 is satisfied by a second even simpler but less
accurate empirical formulae given by
dQ/dt ≈ 91.6 kcal/day (M/kg)
3/4 .
(9.16)
This second relation agrees with the scaling law presented in Sect. 13.4 and so
applies over a wide range of masses. Note: When a process depends linearly on
size, there is an ‘isometric’ relationship, i.e. a proportionality. If the process depends
non-linearly on size, the relationship is called ‘allometric’, from the Greek meaning
different (i.e. not proportional). Amazingly, Eq. (9.16) for the basal metabolism rate
also works reasonably well for other animals from mice all the way to elephants.
(For details, see Sect. 13.4.)
The resting metabolic rate for a male of 53 kg, a height of 188 cm, and an
age of 25 years is typically 75 kcal/h, which is 1800 kcal/day or 87 W. This
corresponds to the consumption of about 16 L of oxygen per hour from the
burning of carbohydrates, fats, and proteins. Inversely, one can measure the oxygen
consumption to find the metabolism rate as
dQ
dt
= 4.69
dV O 2
dt
kcal
L
.
(9.17)
The BMR can be also measured directly by immersion of a patient into an insulated
bath of water whose temperature is recorded.
During sleep, the metabolic rate drops to 65 kcal/h. Hard thinking adds about
22 kcal/h to the BMR. 23 During the act of running, the metabolic rate rises to as
much as 700 kcal/h, but only about 25% of this produces mechanical work during
exercise, i.e. you are hard-pressed to develop more than about 200 W of mechanical
power, which is about a fourth of a horsepower (746 W).
One can determine the overall metabolic heat production by combining the
oxygen consumption, carbon dioxide release, methane release, and nitrogen in urine
through the Brouwer equation (1965). Using data for roosting chickens, he finds
Q = 3.865[O 2 /L] + 1.200[CO 2 /L] − 0.511[CH 4 /L] − 1.431[N/g]
(9.18)
given in kilocalories. 24 Smart farmers know this.
23 Your brain should be getting hotter about now!
24 E. Brouwer, Report of the Subcommittee on Constants and Factors, Energy Metabolism.
Proceeding of the 3rd Symposium, 441–443 [Academic Press] (1965).
339
think of Eq. (9.15) as a straight-line approximation, near human adult masses, to a
full BMR function of mass.
The condition lim M→0 dQ/dt = 0 is satisfied by a second even simpler but less
accurate empirical formulae given by
dQ/dt ≈ 91.6 kcal/day (M/kg)
3/4 .
(9.16)
This second relation agrees with the scaling law presented in Sect. 13.4 and so
applies over a wide range of masses. Note: When a process depends linearly on
size, there is an ‘isometric’ relationship, i.e. a proportionality. If the process depends
non-linearly on size, the relationship is called ‘allometric’, from the Greek meaning
different (i.e. not proportional). Amazingly, Eq. (9.16) for the basal metabolism rate
also works reasonably well for other animals from mice all the way to elephants.
(For details, see Sect. 13.4.)
The resting metabolic rate for a male of 53 kg, a height of 188 cm, and an
age of 25 years is typically 75 kcal/h, which is 1800 kcal/day or 87 W. This
corresponds to the consumption of about 16 L of oxygen per hour from the
burning of carbohydrates, fats, and proteins. Inversely, one can measure the oxygen
consumption to find the metabolism rate as
dQ
dt
= 4.69
dV O 2
dt
kcal
L
.
(9.17)
The BMR can be also measured directly by immersion of a patient into an insulated
bath of water whose temperature is recorded.
During sleep, the metabolic rate drops to 65 kcal/h. Hard thinking adds about
22 kcal/h to the BMR. 23 During the act of running, the metabolic rate rises to as
much as 700 kcal/h, but only about 25% of this produces mechanical work during
exercise, i.e. you are hard-pressed to develop more than about 200 W of mechanical
power, which is about a fourth of a horsepower (746 W).
One can determine the overall metabolic heat production by combining the
oxygen consumption, carbon dioxide release, methane release, and nitrogen in urine
through the Brouwer equation (1965). Using data for roosting chickens, he finds
Q = 3.865[O 2 /L] + 1.200[CO 2 /L] − 0.511[CH 4 /L] − 1.431[N/g]
(9.18)
given in kilocalories. 24 Smart farmers know this.
23 Your brain should be getting hotter about now!
24 E. Brouwer, Report of the Subcommittee on Constants and Factors, Energy Metabolism.
Proceeding of the 3rd Symposium, 441–443 [Academic Press] (1965).