Terrain Factors for Predicting Walking and Load Carriage Energy Costs: Review and Refinement


  • Paul W Richmond U.S. Army Cold Regions Research Engineering Laboratory, Hanover, NH
  • Adam W Potter U.S. Army Research Institute of Environmental Medicine (USARIEM)
  • William R Santee U.S. Army Research Institute of Environmental Medicine (USARIEM)




metabolic cost, modeling, military


The ability to predict the energy cost of load carriage is important to various disciplines and applications including anthropology, exercise physiology, humanitarian aid, and dismounted military operations.  Energy consumption in turn determines the physiological status of individuals and populations and their ability to function via internal heat production, hydration, fatigue, and caloric intake.  Various parameters of the physical environment, including topographic relief and surface conditions impact those energy costs. To be comprehensive, predictive load carriage cost models must incorporate body mass, load, positive and negative grades, and adjustments for surface conditions.  Models developed at the U.S. Army Research Institute of Environmental Medicine (USARIEM) in the 1970s incorporated an adjustment for surface conditions, i.e. a terrain factor.  However, the terrain factors were derived empirically from data for a relatively limited set of surface conditions or classes.  Aside from efforts to apply the classification of terrain factors to a broader set of conditions, little work has been done on to improve terrain factors since the 1970s.  This paper reviews the effect of terrain properties on locomotion, the development of terrain factors, and provides scientific improvements based on the parallel studies of vehicular trafficability at the U.S. Army Cold Regions Research Engineering Laboratory (CRREL).

Author Biography

Adam W Potter, U.S. Army Research Institute of Environmental Medicine (USARIEM)

Adam Potter is a Research Physiologist and Deputy Chief of the Biophysics and Biomedical Modeling Division at the United States Army Research Institute of Environmental Medicine (USARIEM). Mr. Potter served on active duty in the U.S. Marine Corps, participating in real-world operations in Kosovo, Iraq, and Liberia. Prior to working at USARIEM, he performed numerous in-patient clinical research trials. He holds a Bachelor of Arts in Psychology from Cambridge College, a Masters of Business Administration and Master of Science in Sports and Health Sciences from American Military University.  Mr. Potter's current research interests include: thermo-physiology and thermoregulation modeling; estimating metabolic cost over complex terrain; exercise dosimetry for early detection of overuse injuries; and biophysics and clothing impacts on human performance.


Givoni, B. and R. F. Goldman (1971). Predicting metabolic energy cost. J. Appl. Physiol. 30(3): 429-433. 1971.

Soule, R.G. and R.F. Goldman (1972) Terrain coefficients for energy cost prediction. Journal of Applied Physiology, Vol. 32, No. 5, May 1972.

Pandolf, K.B. B. Givoni and R.F. Goldman (1977) Predicting energy expenditure with loads while standing or walking very slowly. J Appl Physiol 43:577-581, 1977.

Pimental, N.A. and K.B. Pandolf (1979) Energy expenditure while standing or walking slowly uphill or downhill with loads, Ergonomics, 22:8, 963-973. http://dx.doi.org/10.1080/00140137908924

Pimental, N.A., Y. Shapiro and K.B. Pandolf (1982) Comparison of uphill and downhill walking and concentric and eccentric cycling, Ergonomics, 25:5, 373-380.

Santee, W.R., L.A. Blanchard, M.G. Small J.A. Gonzalez W.T. Matthew and K.L. Speckman (2001) The impact of load and grade on energy expenditure during load carriage, part II: field study. USARIEM Technical Report T01-11.

Santee W.R., M. G. Small and L.A. Blanchard (2003a) Application of Energy Cost Algorithms for Load Carriage to Field Data. Journal of the Human-Environmental System,Vol. 6; No.2: 69-76. 2003

Passmore, R., and J. V. G. A. Durnin (1955). Human energy expenditure. Physiol. Rev. 35: 801-840. http://physrev.physiology.org/content/35/4/801.full.pdf

Santee, W.R., L.A. Blanchard, K.L. Speckman, J.A. Gonzalez, and R.F. Wallace (2003b). Load Carriage Model Development and Testing with Field Data. Technical Note No. TN03-3, U.S. Army Research Institute of Environmental Medicine, Natick, MA.

Lejeune, T.M., P.A. Willems and N.C. Heglund (1998) Mechanics and energetic of human locomotion on sand. The Journal of Experimental Biology 201, 2071–2080 (1998)

Crowell, H.P. III; A.S. Krausman, W.H. Harper, J.A. Faughn, M.A. Sharp, R.P. Mello, T. Smith, J.F. Patton (1999) Cognitive and Physiological Performance of Soldiers While They Carry Loads Over Various Terrains. ARL-TR-1779, U.S. Army Research Laboratory, Human Research & Engineering Directorate, Aberdeen Proving Ground, MD.

Zamparo, P., R. Perini, C. Orizio, M. Sacher, G. Ferretti (1992) The energy cost of walking or running on sand. European Journal of Applied Physiology and Occupational Physiology 65:2:183-187. http://dx.doi.org/10.1007/BF00705078

Strydom, N.B., G.A. G. Bredell, A.J.S. Benade, J.F. Morrison, J.H. Viljoen, and C.H. Van Graan (1966) The Metabolic Cost of Marching at 3 M.P.H. Over Firm and Sandy Surfaces. Int. Z. angew. Physiol. einschl. Arbeitsphysiol. 23, 166-171 (1966)

Winsmann, F.R. and F. Daniels, Jr. (1956) Pack Carrying in the Desert. Technical Report EP 28. U.S. Army Quartermaster Center, Natick, MA.

Daniels, Jr., F., J.H. Vanderbie, and F.R. Winsmann (1953) Energy cost of treadmill walking compared to road walking. Report 220, Natick QM Research & Development Laboratory, Lawrence, MA.

Miller, J.M. (1983)."Slippery" work surfaces: Towards a performance definition and quantitative coefficient of friction criteria." J. Safety Res. 14(4): 145-158.

Rush, E.S. and A.A. Rula (1967) A limited study of effects of soil strength on walking speed. Miscellaneous Paper No. 4-950, U.S. Army Waterways Experiment Station, Vicksburg, MS.

Soule, R.G and C.K. Levy (1972) Voluntary march rate over natural terrains. Federation Proceedings Abs. 31,312.

Bullock, C.D. (1994) Methodology for the Development of Inference Algorithms for Worldwide Application of Interim Terrain Data to the NATO Reference Mobility Model. Technical Report GL-94-37, Waterways Experiment Station, Vicksburg, MS.

Durst, P.J., G.L. Mason, B. McKinley, and A. Baylot (2010) Predicting RMS surface roughness using fractal dimension and PSD parameters. J. Terramechanics 2010 doi:10.1016/j.jterra.2010.05.004.

Durst, P.J., A. Baylot, B. McKinley, and G.L. Mason (in press) A General Model for Inferring Terrain Surface Roughness as a Root-Mean-Square to Predict Vehicle Off-Road Ride Quality. Int. J. Vehicle Design, in press.

Voloshina, A.S. A.D. Kuo, M.A. Daley, D.P. Ferris (2012) Biomechanical and Energetic Consequences of Walking on Uneven Terrain. Presented at the Dynamic Walking Conferece May 2012, Pensacola, FL. http://dynamicwalking.org/dw2012/, video of presentation: http://www.youtube.com/watch?v=dfPNUGlBd5A and extended abstract: http://www.ihmc.us/dwc2012files/Voloshina.pdf

Voloshina, A. S., & Ferris, D. P. (2015). Biomechanics and energetics of running on uneven terrain. The Journal of experimental biology (accepted).

Paysant, J., C. Beyaert, A-M. Datie, N. Martinet, and J-M. Andre (2006) Influence of terrain on metabolic and temporal gait characteristics of unilateral transtibial amputees. Journal of Rehabilitation Research & Development, 43:2,153-160.

White, R.G., and M.K. Yousef (1978) Energy expenditure in reindeer walking on roads and on tundra. Can. J. Zool. 56: 215-223.

Amor, A F. and J.A. Vogel (1974) Energy Cost of Man-Packing the Swingfire Missile, Army Personnel Research Establishment Farnborough (United Kingdom), Jan-1974, ADB001376

Friedl , K., and Santee, W. R. (2012). Military Quantitative Physiology: Problems and Concepts in Military Operational Medicine. Government Printing Office.

Minetti, A.E., C. Moia, G.S. Roi, D. Susta and G. Ferretti (2002) Energy cost of walking and running at extreme uphill and downhill slopes. J. Appl. Physiol. 93:1039-1046, doi: 10.1152/japplphysiol.01177.2001

Minetti, A.E., L.P. Ardigo, E.M. Capodaglio and F. Saibene (2001) Energetics and Mechanics of Human Walking at Oscillating Speeds. Amer. Zool., 41:205–210 (2001)

Jobe, R. T., and P. S. White (2009) A new cost-distance model for human accessibility and an evaluation of accessibility bias in permanent vegetation plots in Great Smoky Mountains National Park, USA, J Vegetation Sci 20:6, 1099-1109.




How to Cite

Richmond, P. W., Potter, A. W., & Santee, W. R. (2015). Terrain Factors for Predicting Walking and Load Carriage Energy Costs: Review and Refinement. Journal of Sport and Human Performance, 3(3). https://doi.org/10.12922/jshp.v3i3.67



Original Research Articles