Predicting metabolic cost of running with and without backpack loads

Y. Epstein*, L. A. Stroschein, K. B. Pandolf

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 <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: {Mathematical expression} 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.

Original languageEnglish
Pages (from-to)495-500
Number of pages6
JournalEuropean Journal of Applied Physiology and Occupational Physiology
Issue number5
StatePublished - Sep 1987
Externally publishedYes


  • Backpack load
  • Load carriage
  • Metabolic cost
  • Prediction model
  • Running
  • Work efficiency


Dive into the research topics of 'Predicting metabolic cost of running with and without backpack loads'. Together they form a unique fingerprint.

Cite this