Measurements of vertical displacement in running, a methodological comparison Lennart Gullstrand a,b, *, Kjartan Halvorsen c,d , Fredrik Tinmark c , Martin Eriksson d , Johnny Nilsson c,e a Elite Sports Centre, Boso ¨n Swedish Sports Confederation, Lidingo ¨, Sweden b Section of Exercise Physiology, Department of Physiology and Pharmacology, Karolinska Institutet, Stockholm, Sweden c Biomechanics and Motor Control Laboratory, Department of Sport and Health Sciences, The Swedish School of Health and Sports Sciences, Stockholm, Sweden d School of Technology and Health, Royal Institute of Technology, Stockholm, Sweden e Norwegian School of Sport Sciences, Oslo, Norway 1. Introduction Running economy (RE) is defined as total oxygen consumption in mL kg 1 min 1 during running at a given submaximal, steady state velocity [1]. Factors influencing running economy may be of physiological [2] and biomechanical [3] origin and is related to training adaptations [4]. Further investigations are needed to explain the effect of each sub-factor on RE. These effects appear to be both complex and individual [5]. It seems plausible, that all movements diverging from the running direction will affect the RE negatively, especially so in exaggerated vertical displacement (V disp ) of the centre of mass (CoM). Thorstensson et al. [6] showed that movements in the medio-lateral directions are smaller than in the vertical direction and probably have less influence on the RE. Williams and Cavanagh [7], reported that elite distance runners exhibited a somewhat lower (not significantly) V disp compared to non-elite distance runners. Heise and Martin [8] found that total vertical force impulse correlate negatively with RE. The vertical impulse is proportional to the change in vertical velocity of CoM, and hence directly related to the V disp of the CoM. The V disp causes a demand in mechanical power, P v = sfmgV disp , where sf is the step frequency, m is the mass of the body, and g is the gravitational acceleration. This is the power required to lift the CoM a distance V disp at a certain rate. Part of this power may come from the release of potential energy stored in elastic components of the body (and shoes) [3,4]. In running there are energy transfers occurring in each cycle between kinetic and potential energy, both in the form of CoM height and stretched or compressed elastic components. The actual amount of energy that is dissipated during these transfers (and that hence must be compensated by work of the muscles) is not fully known. However, if we assume that the amount of energy dissipated correlates positively with the actual fluctuation of potential energy, it makes sense to focus on the V disp of CoM as relevant for RE. As a numeric example, a reduction of V disp with 1 cm at a step frequency of 200 min 1 reduces the mechanical power by 22 W and may improve RE with some 0.3 L min 1 for a person with a body mass of 67.3 kg. Consequently, methods to measure V disp accurately and in a simple manner is relevant, in order to analyse and monitor P v and relate this to RE. In the case of level walking, measuring the V disp of a single point on the sacrum has been shown to perform equally well as Gait & Posture 30 (2009) 71–75 ARTICLE INFO Article history: Received 1 July 2008 Received in revised form 6 November 2008 Accepted 4 March 2009 Keywords: Vertical displacement Treadmill running Running economy ABSTRACT The aim was (1) to evaluate measurements of vertical displacements (V disp ) of a single point on sacrum as an estimate of the whole body centre of mass (CoM) V disp during treadmill running and (2) to compare three methods for measuring this single point. These methods were based on a position transducer (PT), accelerometers (AMs) and an optoelectronic motion capture system. Criterion method was V disp of the whole body CoM measured with the motion capture system. Thirteen subjects ran at 10, 12, 14, 16, 18, 20 and 22 km h 1 with synchronous recordings with the three methods. Four measurements of the (V disp ) were derived: (1) V disp of CoM calculated from a segment model consisting of 13 segments tracked with 36 reflective markers, (2) V disp of the sacrum recorded with the PT, (3) V disp of the sacrum calculated from the AM, and (4) V disp of the sacrum calculated as the mid point of two reflective markers (sacrum marker, SM) attached at the level of the sacral bone. The systematic discrepancy between the measurements of sacrum V disp and CoM V disp varied between 0 and 1.5 mm and decreased with increasing running velocity and decreasing step duration. PT and SM measurements showed strong correlation, whereas the AM showed a variability increasing with velocity. The random discrepancy within each subject was 7 mm for all three methods. In conclusion single-point recordings of the sacrum V disp may be used to monitor changes in V disp of CoM during treadmill running. ß 2009 Elsevier B.V. All rights reserved. * Corresponding author at: Elite Sports Centre, Boso ¨ n Swedish Sports Confedera- tion, 181 47 Lidingo ¨, Sweden. Tel.: +46 8 699 66 56; fax: +46 8 699 60 88. E-mail address: lennart.gullstrand@rf.se (L. Gullstrand). Contents lists available at ScienceDirect Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.03.001