Volume 49, Issue 16, 8 December 2016, Pages 4150–4153

Short communication

A simple model for predicting walking energetics with elastically-suspended backpack

  • a State Key Laboratory of Fluid Power and Mechatronic Systems, College of Mech. Eng., Zhejiang University, 310027 Hangzhou, China
  • b Department of Mechanical and Materials Engineering, Queen׳s University, Kingston, ON, Canada
  • c Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA


An elastically-suspended backpack offers biomechanical benefits by reducing peak interaction force, joint loads and chances of potential injuries as shown in previous studies. But whether it will reduce metabolic cost of the carrier (compared with the stiffly-attached pack) depends on the relation between the natural frequency of the suspension and walking frequency. Yet, no quantitative method can precisely evaluate to what extent the elasticity of suspension affects human walking energetics. We employ a single degree of freedom (DOF) model to quantitatively evaluate the effect of stiffness and damping of pack on human energetics. A surrogate of metabolic cost is proposed and utilized to estimate the energetics difference between carrying backpacks of different stiffness. The predicted difference is consistent with former backpack studies. The analysis reveals that the energy cost increases around the resonant frequency and the difference gets more significant at higher walking speeds or with heavier loads. This method gives closer energetic estimation compared with previous studies. Yet there is potentially an underestimation of the energy difference indicating later models should contain horizontal motion to obtain more precise prediction.


  • Energetics;
  • Load carriage;
  • Backpack;
  • Elasticity;
  • Walking

1. Introduction

Although transportation technology has been much advanced, walking with packs is still inevitable, especially for those hikers, soldiers or students (Knapik et al., 2004, Ren et al., 2005 and Rome et al., 2006). One of the most important factors in load carriage is energetics. Less energy consumption means the capability for longer distance and heavier loads (Rome et al., 2006).

Human energetics of load carrying is affected by many factors including load distribution, weight of the load, walking (or running) speed, etc. (Abe et al., 2004). Early researchers mainly focused on the effect of different load-carrying methods including using head-packs, yokes, hands, etc. (Balogun, 1986, Datta and Ramanath, 1971 and Ramanath et al., 1972) and load distribution (on back, legs or hands) (Legg and Mahanty, 1985, Obusek et al., 1997 and Soule and Goldman, 1969).

Recently, the elasticity of linkage between load and the carrier was explored and it was proved to be able to offer considerable biomechanical benefits by reducing the peak interaction force, joint forces and potential injuries when decreasing the stiffness of backpack linkage (Ren et al., 2005 and Rome et al., 2006). A few studies also showed that carrying load elastically can reduce the energy cost of walking. Rome et al. (2006) designed a backpack which cost 6.25% less energy in elastically-suspended mode than that in stiffly-fixed mode. Compliant poles were also found to be more energy-saving than steel poles during walking with load (Castillo et al., 2014). Similarly, a legged robot cost less energy while carrying load with elastic suspension (Ackerman and Seipel, 2013). Foissac et al. (2009), however, found carriers consumed more energy with a flexible backpack than a rigid one when walking at 5.2 Km/h and 6 Km/h. Ren et al. (2005) carried out an simulation of carrying backpack with different stiffness but found that stiffness and damping of backpack had little effect on energetics.

Ackerman and Seipel (2014) employed a two-DOF model to explain the conflict experimental results on energy cost in previous studies (Foissac et al., 2009 and Rome et al., 2006). Net mechanical work from the assumed leg actuator in a stride, which was treated as an indirect indicator of energy cost, increased and decreased over 60% when carrying the flexible backpack compared with the work of carrying the rigid pack using parameters in previous experiments by Foissac et al. (2009) and Rome et al. (2006) respectively. However, the energetics difference between carrying packs of different stiffness was found less than 10% in previous experiments. There still lacks a method that can accurately estimate the energy cost of carrying load with elastic suspension.

The purpose of this paper is to provide an alternative method to quantitatively evaluate the influence of the elasticity of backpack on human energetics. Horizontal motion is assumed to be unaffected for different suspension and mechanical work on center of mass (COM) was reported to be correlated with the body metabolism (Kramer and Sylvester, 2011). Hereby the mechanical work required by vertical motion is treated as a surrogate of energy cost. Different from the study by Ackerman and Seipel (2014), we take the efficiency of the muscle performing mechanical work into consideration when calculating the energy cost of backpack carriage. It׳s expected that in this way less discrepancy between the model predictions and energy cost measurements in previous experiments will be obtained.

2. Methods

The single degree-of-freedom (DOF) spring-mass-damper model in Fig. 1(A) was used to assess the performance of elastically-suspended backpack in the previous study by Hoover and Meguid (2011). The equivalent spring and damper were proved to be effective to characterize the kinematics of the vertical interaction between the carrier and the backpack. The equation of motion of this simple vibration model is:

View the MathML source
where x denotes the sinusoidal movement of the body COM, and its amplitude (X) and frequency (ω) both vary with respect to the walking speed and can be calculated with empirical equations ( Hoover and Meguid, 2011). And y is the movement of the backpack excited by the motion of body. The stiffness k and damping c are the equivalent spring constant and damping coefficient.