Minetti et al. 2002, energy cost of walking and running at extreme slopes

Treadmill study (J Appl Physiol) measuring the energy cost of walking and running across gradients from −45% to +45% in ten runners. On the level, running cost about 3.40 J·kg⁻¹·m⁻¹ and walking about 1.64. Both rise steeply uphill. At the steepest +45% gradient the minimum cost of walking (17.33 J·kg⁻¹·m⁻¹) was lower than that of running (18.93), so above a critical incline walking becomes the more economical gait, the physiological basis for power-hiking steep climbs. Downhill, cost falls to a minimum then rises again as braking demand grows.