MECHANICAL EFFICIENCY, WORK AND HEAT OUTPUT IN RUNNING UPHILL OR DOWNHILL - Pietro Enrico di Prampero (ANNALES ZRS, Scientific Publishing House of ZRS Koper, 2015)
Heat output in running, per unit distance and body mass, was evaluated from published data on the corresponding energy cost (Cr). Cr is independent of the speed and is a function incline (i);  between i = - 0.45 and + 0.45, it is described by Cr = 155.4 i5 - 30.4 i4 - 43.3 i3 + 46.3 i2 + 19.5 i + 3.6, where 3.6 J/(kg m) is the cost on flat terrain (Minetti et al., 2002). Since the mechanical work performed against gravity is proportional to it, this equation allows one to calculate the efficiency (h) of work performance against gravity: h increases with i to attain a value of about 0.23 for i ≥ 0.25. When running downhill, h becomes negative to attain a value of about - 1.0 for i = - 0.25 or steeper. Cr is transformed into mechanical work (w) and/or dissipated as heat (h): Cr = w + h. Since h = w/Cr, h, per unit mass and distance, can be calculated for any given slope and speed (h = Cr - w = Cr (1 - h)). The minimum Cr (2.28 J/(kg m)) is attained for i ≈ - 20 %, whereas the minimum h (3.53 J/(kg m)) for i ≈ - 8 %. Furthermore, since both Cr and h are independent of the speed, the ratio h/Cr, which ranges from about 2 (for i = - 0.40) to 0.77 (for i = + 0.40), at any given speed is equal to the ratio of heat output to metabolic power rates.