Running Uphill

Earlier, we talked about the power required for bicycling uphill.  Today we’ll talk about the same effects for running uphill.
In some ways, bicycling uphill and running uphill are very similar.  The equations for power needed to overcome air resistance and to change elevation are, of course, identical.  It is more common in running to express speed as a pace, e.g. minutes per mile, rather than as a speed, e.g. miles per hour.  However, that is really just a matter of converting units.  The biggest difference between running and cycling power estimations lies in the “base” energy use.  For bicycling, this is mostly the power required to overcome rolling resistance.  The analogous quantity for running would be the power required to run at a steady pace on flat ground.  Unfortunately, for running, that is a very difficult quantity to estimate accurately for any particular individual. It depends on a lot of variables.  For example, fitness level, weight, weight distribution (around waist or in calves), air temperature, running surface, biological sex, and others all have an effect on that base energy use.

For our purposes today (looking at the effect of grade) we might assume that whatever the base power level is for a particular individual, it will be constant for a particular day.  In order to get a representative value for the base power, we can use the very rough rule-of-thumb of 100 Cal/mile energy expenditure coupled with a 15% conversion efficiency.  Once we’ve made that assumption, we can look at the effect of grade on power requirements.  

This figure shows 2 different paces at 3 different uphill grades. 

 Remember that the selection of the base power use was pretty arbitrary.  A different value for base power would shift all of the up or down, but the relative positions would stay the same.  In other words, this figure is useful for comparisons between paces or grades, but probably not very accurate in absolute terms.

This figure demonstrates the breakdown between base power, air resistance, and climbing power for a 7 minute pace on a 6% grade.  

As one would expect, the air resistance is only a minor contribution to the overall power requirement.
 
Next time we’ll look at how pace is affected by weight and grade for a given power expenditure.