Given a certain running pace uphill, I want to be able to determine an equivalen

Question

Given a certain running pace uphill, I want to be able to determine an equivalent pace running with no elevation change. Assumptions: similar effort in both cases (say for example running at 90% max heart rate), ignore wind, slope is constant for simplicity, ignore physiological and bio-mechanical factors, weight of the runner is 135 lbs if that matters.

Example: Elevation change +236 feet, distance traveled 1 mile, elapsed time 6 minutes 55 seconds. What could I theoretically run for 1 mile with no elevation change given the same effort?

Explanation / Answer

The easiest (and roughest) way to to do it would be to convert your running "work" into a VO2 score.

The American College of Sports Med's equation is

VO2= Resting Component + Horizontal Component + Vertical Component or VO2= 3.5 + (0.2 x Speed) + (0.9 x Speed x Elevation Gain)

So, using your example of 8.67 mph (speed in the equation is in meters per min)

3.5 + (.2*232.67) + (0.9*232.67*.045) = 59.5

Thus running on flat ground should give you a speed of 280 m/min or 10.44 mph 5 min 44 sec per mile

(I'm an exercise scientist, not a physicist)

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