Investigation of the pedaling forces in a cycling field test using the non-linear measure ML1

Abstract

The study of biomechanical and physiological variables allows human movement scientists to investigate the characteristics of movement patterns in cyclists. While straightforward and well-investigated, linear measures may not adequately capture the underlying complexity of movements during cycling. Therefore, a non-linear phase-space measure (ML1) was applied to forces and heart rates of nine cyclists in a field test. The test was repeated two times with different instructions on how to alter the bike’s gearing while cycling a 12.5 km long level track. Pedaling forces and heart rates were measured. Future aim of the underlying study is the investigation of innovative control algorithms for e-bike propulsions. Force-time curves were sequenced into single cycles, linearly interpolated in the time domain, and z-score normalized. ML1 was calculated in a flowing window algorithm of 50 cycles. With fixed gearing, a contrast analysis showed that changes in terrain inclination were strongly associated with changes in the non-linear measure ML1. The calculation of Spearman’s cross correlation showed high coefficients of correlation between ML1 and delayed heart rate. The results indicate systematic changes of the pedaling movement as an adaptive response to changes in terrain inclination. Future research may utilize the findings from this study to investigate possible relationships between subjective measures of exhaustion, comfort, and discomfort with biomechanical characteristics of the pedaling movement.

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“…This may also be the reason for the clearer linear increase of ML 1 F compared to ML 1 α in the results even in the current laboratory test. This is also suggested in [ 11 ], where a replication of ML 1 F within indoor and outdoor tests was shown—despite external disturbance factors and additional vibrations. However, the disadvantage of ML 1 α in field applications remains hypothetical at this point and should be further investigated in field studies.…”

“…According to a first assessment, a length of about 75 to 100 cycles seems to be necessary. This corresponds to a slightly longer time series than the length proposed in [ 11 ] for ML 1 F . Nevertheless, further research is needed.…”

“…Previous studies have investigated heterogeneous groups [ 10 , 11 ]. Therefore, we did not focus on typical e-bike users to generate a more homogenous group regarding age and ability.…”

“…The novel ML 1 method was applied to the pedaling forces using a sliding window algorithm [ 10 , 11 ]. The window width was set to 50 normalized cycles (interpolation to 100 samples per cycle), representing 5000 points in phase space (see Fig 1 ).…”

“…In previous studies [ 10 , 11 ], we analyzed crank forces and developed a nonlinear parameter that correlates with the individual load when, for example, changes in terrain inclination are prevalent. This parameter, called ML 1, is defined by the vector length of the geometric median of the force points in two dimensional phase space.…”