Predicting metabolic cost of running with and without backpack loads

Eur J Appl Physiol Occup Physiol. 1987;56(5):495-500. doi: 10.1007/BF00635360.


In the past, a mathematical equation to predict the metabolic cost of standing or walking (Mw) was developed. However, this equation was limited to speeds less than 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 (Mr), 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 Mw and is proportionately linear with external load (L) carried as follows: Mr = Mw-0.5 (1-0.01L)(Mw -15L-850), (watt) The correlation coefficient between predicted and observed values was 0.99 (P less than 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 less than 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.

MeSH terms

  • Adult
  • Energy Metabolism*
  • Humans
  • Male
  • Mathematics
  • Military Personnel
  • Models, Biological*
  • Running*