Dear Biomch-l

It is a common observation that one becomes hot when climbing a mountain
but not when descending it. In climbing, the low efficiency of energy
conversion in muscles means that for every Joule of external mechanical
work, several Joules must be dissipated as heat. This can be described

Heat = metabolic work rate - rate of external work by muscles (1a)
Heat = metabolic work rate - rate of potential energy gain (1b)

In descending, the muscles mainly work eccentrically by absorbing the
potential energy of the body and converting it (again inefficiently)
into heat. This can be expressed as:

Heat = metabolic work + rate of potential energy loss (2)

However, since descent occurs much faster than ascend, I have often
wondered what are the relative magnitudes of these energy rates, and
whether the amount of potential energy loss when descending fast might
be manifested as a noticeable heat dissipation problem.

Quantitatively, the text by Inman, Ralston and Todd (Human Walking,
Williams and Wilkins, 1981) offers some insights. It gives (in Table
3.7 on page 70) the metabolic energy in cal/min/kg for ascent and
descent of various grades at differing speeds. Taking as an
illustrative example, a 25% (14 degree) grade which is climbed at 40
m/min and descended at 80 m/min. The metabolic work in ascending is 114
cal/min/kg and a simple calculation gives the rate of potential energy
gain as 23 cal/min/kg

so net heat output = 114 - 23 = 91 cal/min/kg.

In descending, the metabolic work is 63 cal/min/kg and the mechanical
potential energy loss is 46 cal/min/kg

so net heat output = 63 + 46 = 109 cal/min/kg.

Therefore, this simple calculation suggests that one should need to
dissipate more heat (109 compared to 91 cal/kg/min) and might
subjectively feel hotter in descending than ascending. Clearly, there
are at least two confounding factors. Firstly, both convection and
evaporated heat loss should work better when traveling faster.
Secondly, there are sure to be frictional losses between footwear and
the ground and the terrain, resulting in energy input into the terrain
rather than the human body. Despite this, I would be interested to know
whether others regard this as a biomechanical paradox.

Ian Stokes