Change in geometric entropy with repeated ascents in rock climbing

ABSTRACT

Lower geometric entropy (GE) could represent more economical movement in rock climbing. Repetition of a climbing route decreases energy expenditure (EE), however, association with changes in GE has not been studied. The purpose of this study was to observe changes in GE with repetition of a climbing route relative to changes in EE. Nine climbers completed nine ascents each, one week apart, on an indoor climbing structure. Digital video was recorded at 30 Hz and a marker point was digitised as an estimate of a climber’s centre of mass position (CM_E). The displacement of CM_E was expressed as the length of the line of motion (LM). GE was calculated as ln((2 x LM)/CH)) where CH is the value of the convex hull about the LM. Indirect energy expenditure (EE_CLM) was calculated from expired air by the Weir method. Data were analysed for ascents 1 (A1), 3 (A3), 6 (A6) and 9 (A9) and compared via repeated measures ANOVA. GE was significantly different for A1 vs A6 and A9 (p < 0.05) and not different for other comparisons. GE was correlated with EE_CLM; r = 0.67 (p < 0.01). Climbers reduce geometric entropy with route familiarity and the lower entropy may be associated with lower energy expenditure.

KEYWORDS:

• Economy
• energy expenditure
• geometric entropy
• rock climbing

Acknowledgments

The authors are indebted to Mr Matt Kilgas, Exercise Science Laboratory of Northern Michigan University for assistance in completing manual digitisation of the video for this study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Partially funded by Northern Michigan University Faculty Grant 5-54832