Predicting metabolic cost of running with and without backpack loads

In the past, a mathematical equation to predict the metabolic cost of standing or walking (M_w) was developed. However, this equation was limited to speeds <2.2 m · s⁻¹ and overestimated the metabolic cost of walking or running at higher speeds. The purpose of this study was, therefore, to develop a mathematical model for the metabolic cost of running (M_r), in order to be able to predict the metabolic cost under a wide range of speeds, external loads and grades. Twelve male subjects were tested on a level treadmill under different combinations of speed and external load. Speed varied between 2.2 to 3.2 m · s⁻¹ using 0.2 m · s⁻¹ intervals and external loads between 0–30 kg with 10 kg intervals. Four of the subjects were also tested at 2 and 4% incline while speed and load remained constant (2.4 m · s⁻¹, 20 kg). The model developed is based on M_w and is proportionately linear with external load (L) carried as follows: $$M_r = M_w - 0.5(1 - 0.01L)(M_w - 15L - 850), (watt)$$ The correlation coefficient between predicted and observed values was 0.99 (P<0.01) with SER of 7.7%. The accuracy of the model was validated by its ability to predict the metabolic cost of running under different conditions extracted from the literature. A highly significant correlation (r=0.95,P<0.02, SER=6.5%) was found between our predicted and the reported values. In conclusion, the new equation permits accurate calculation of energy cost of running under a large range of speeds, external loads and inclines.