Applying the cost of generating force hypothesis to uphill running

Historically, several different approaches have been applied to explain the metabolic cost of uphill human running. Most of these approaches result in unrealistically high values for the efficiency of performing vertical work during running uphill, or are only valid for running up steep inclines. The purpose of this study was to reexamine the metabolic cost of uphill running, based upon our understanding of level running energetics and ground reaction forces during uphill running. In contrast to the vertical efficiency approach, we propose that during incline running at a certain velocity, the forces (and hence metabolic energy) required for braking and propelling the body mass parallel to the running surface are less than during level running. Based on this idea, we propose that the metabolic rate during uphill running can be predicted by a model, which posits that (1) the metabolic cost of perpendicular bouncing remains the same as during level running, (2) the metabolic cost of running parallel to the running surface decreases with incline, (3) the delta efficiency of producing mechanical power to lift the COM vertically is constant, independent of incline and running velocity, and (4) the costs of leg and arm swing do not change with incline. To test this approach, we collected ground reaction force (GRF) data for eight runners who ran thirty 30-second trials (velocity: 2.0–3.0 m/s; incline: 0–9°). We also measured the metabolic rates of eight different runners for 17, 7-minute trials (velocity: 2.0–3.0 m/s; incline: 0–8°). During uphill running, parallel braking GRF approached zero for the 9° incline trials. Thus, we modeled the metabolic cost of parallel running as exponentially decreasing with incline. With that assumption, best-fit parameters for the metabolic rate data indicate that the efficiency of producing mechanical power to lift the center of mass vertically was independent of incline and running velocity, with a value of ～29%. The metabolic cost of uphill running is not simply equal to the sum of the cost of level running and the cost of performing work to lift the body mass against gravity. Rather, it reflects a constant cost of perpendicular bouncing, decreased costs of parallel braking and propulsion and of course the cost of lifting body mass against gravity.