It is a common observation that one becomes hot when climbing a mountain but less so when descending it. How can this be consistent with the energy balance?
When hiking uphill the heat generated does NOT include the elevation gain:
Heat generated = metabolic work rate - rate of external work by muscles or equivalently
Heat generated = metabolic work rate - rate of potential energy gain
= metabolic work rate - mass * gravity * climbing rate
In descending, the muscles mainly work by absorbing the potential energy of the body and pack and converting it into heat (negative work). This can be expressed as:
Heat = metabolic work rate + rate of potential energy loss
= metabolic work rate + mass * gravity * descending rate
Given that the potential energy change (force times distance) is the same going up and down and that this is subtracted from the heat generation going up and added going down - one should become warmer when going down relative to going up, like the brakes on your car. This is just the opposite of everyday experience creating an interesting paradox (at least if one is a nerdy engineer who thinks about such things).
Johnson et al., 2002 measured energy efficiency and heat generation when walking up and down hill at a constant velocity.
Eight subjects wearing insulating clothing walked on a treadmill at three uphill and three downhill grades,and at level grade at a rate of 1.1 m/s. Oxygen consumption was calculated from steady state measurements of respiratory volume and oxygen percentage. Efficiency is dependent upon the slope or grade. The efficiency is zero at zero grade because no net work is being performed (i.e., the weight of body, clothes, and pack do not change elevation).
The body performs negative work going down hill (i.e., braking) at about twice the efficiency of uphill work and that explains why going uphill generates more heat. Steeper grades are negotiated more efficiently (at least in terms of oxygen use and metabolism) than gentle grades.
The overall results from Johnson et al., 2002 are plotted below for amount of heat generation and oxygen consumption. Oxygen consumption should be proportional to the amount of muscular effort whereas heat generation includes the muscular effort as well as the heat from "braking" when going downhill. That is why the oxygen and heat curves follow each other going uphill but diverge going downhill. In both cases the results are normalized using(divided by) the value for walking on flat ground.
The results are consistent with everyday experience. Walking downhill on a very gentle grade of 5% or less is very easy (low oxygen consumption) and allows one to cool off. Steep downhill walking requires somewhat less effort than steep uphill walking (i.e., one does not get so out of breath), but is 2/3 as warm as walking uphill and does require significant physical effort.
In terms of oxygen consumption, the most efficient walking is at a grade of -5 to -15%, gentle downhill. At the same grade or slope, about half as much oxygen is used going down as going up, even though the same amount of work is being done by the body. About 2/3 as much heat is generated when walking downhill relative to the same grade going uphill. In my experience the oxygen curve is consistent with how tired one becomes when walking at the different slopes. May all hikes be on gentle downhill grades (except after the holidays when I need to lose weight).
Johnson, Arthur T., M. Benhur Benjamin, Nischom Silverman, Oxygen consumption, heat production, and muscular efficiency during uphill and downhill walking, Applied Ergonomics 33 (2002)485 –491.