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The bouncing mechanism of running against hindering, or with aiding traction forces: a comparison with running on a slope

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Abstract

Purpose

Much like running on a slope, running against/with a horizontal traction force which either hinders/aids the forward motion of the runner creates a shift in the positive and negative muscular work, which in turn modifies the bouncing mechanism of running. The purpose of the study is to (1) investigate the energy changes of the centre of mass and the storage/release of energy throughout the step during running associated with speed and increasing hindering and aiding traction forces; and (2) compare these changes to those observed when running on a slope.

Methods

Ground reaction forces were measured on eight subjects running on an instrumented treadmill against different traction forces at different speeds.

Results

As compared to unperturbed running, running against/with a traction force increases/decreases positive external work by ~ 20–70% and decreases/increases negative work by ~ 40–60%, depending on speed and traction force. The external power to maintain forward motion against a traction is contained by increasing the pushing time and step frequency. When running with an aiding force, the external power during the brake is limited by increasing braking time. Furthermore, the aerial time is increased to reduce the power required to reset the limbs each step.

Conclusion

Our results show that the bouncing mechanism of running against/with a hindering/aiding traction force is equivalent to that of running on a positive/negative slope.

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Modified from di Prampero et al. (2005)

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Abbreviations

\({a_{\text{l}}} {, } {a_{\text{f}}} , {a_{\text{v}}}\) :

Lateral, fore-aft and vertical accelerations of the CoM

\(\user2{ }{\overline{a}_{\text{v,ce}}}\) , \(\user2{ }{\overline{a}_{\text{v,ae}}}\) :

Average vertical acceleration of the CoM during the tce and tae

ATF, HTF:

Aiding traction force, hindering traction force

BW:

Body weight

BW// :

Component of the body weight vector parallel to the slope of the terrain

CoM:

Centre of mass of the body

Ecom = Ekf + Ev :

Mechanical energy of the CoM due to its movements relative to the surroundings

\({E_{{\text{kf}}}}\) :

Kinetic energy of the CoM due to its fore-aft velocity

E v :

Mechanical energy of the CoM due to its vertical movements

f s :

Natural frequency of the body bouncing system

\({\overline{F}_{{\text{brake}}}}\) , \({\overline{F}_{{\text{push}}}}\) :

Average forces during the negative (brake) and positive (push) work phases

F f :

Resultant of the fore-aft forces applied on the body

F tr :

Horizontal component of the traction force

Fl, Fh, Fv :

Lateral, horizontal and vertical components of the GRF

\({\overline{F}_{\text{h}}}\) :

Average of Fh over a stride

\({\overline{F}_{\text{v}}}\) :

Average of Fv over a stride

g :

Acceleration of gravity

GRF:

Ground reaction force

k :

Stiffness of the elastic structures responsible for the rebound

m :

Body mass

\({\overline{P}_{\text{f}}}\) :

Average power spent to maintain the fore-aft movements of the CoM

\({\overline{P}_{\text{s}}}\) :

Average power spent on a slope

\({\overline{P}_{{\text{tr}}}}\) :

Average power spent to overcome the traction force

\({\overline{P}_{\text{v}}}\) :

Average power spent to maintain the vertical movements of the CoM

%R :

Percentage of energy transduction between Ev and Wf

\({s_{\text{v}}}\) :

Vertical displacement of the CoM

T :

Step period

t ae, t ce :

Effective aerial time and effective contact time, i.e., respectively, the period during which Fv < BW, and Fv > BW

t a, t c :

Aerial time and contact time

t push, t brake :

Duration of \({W_{{\text{ext}}}}^{ + }\) and \({W_{{\text{ext}}}}^{ - }\)

Unperturbed running:

Running on the level at a constant average speed, without a traction force

\({v_{{\text{belt}}}}\) :

Speed of the treadmill belt

\({V_{{\text{belt}}}}\) :

Average speed of the treadmill belt over a stride

\({v_{\text{l}}}\), \({v_{\text{f}}}\), \(v_{{\text{v}}}\) :

Lateral, fore-aft, and vertical components of the velocity of the CoM

\({\overline{v}_{\text{f}}}\) :

Average of \({v_{\text{f}}}\) over a stride

\({\overline{v}_{\text{v}}}\) :

Average of \({v_{\text{v}}}\) over a stride

\({W_{{\text{ext}}}}\) :

External work, i.e., the work done to sustain the movements of the CoM relative to the surroundings plus the work done on/by the traction force

\({W_{{\text{ext}}}}^{ + }\), \({W_{{\text{ext}}}}^{ - }\) :

Positive and negative work phases of \({W_{{\text{ext}}}}\)

\({\dot{W}_{{\text{ext}}}}\) :

External power, i.e., the time-derivative of \({W_{{\text{ext}}}}\)

\({\dot{W}_{\text{int}}}\) :

Internal power, i.e., the power necessary to move the limbs relative to CoM

\({W_{\text{f}}}\) :

Work done at each instant to sustain the fore-aft movements of the CoM plus the work to overcome the traction force

\({W_{\text{f}}}^{ + }\),\({ W_{\text{f}}}^{ - }\) :

Positive and negative work phases of \({W_{\text{f}}}\)

\({W_{\text{v}}}^{ + }\),\({W_{\text{v}}}^{ - }\) :

Positive and negative work done to sustain the vertical movements CoM relative to the surroundings

\({W_{{\text{tr}}}}\) :

External work done on/by the traction force

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Acknowledgements

This study was funded by the Université catholique de Louvain (UCLouvain-Belgium), and the Fonds de la Recherche Scientifique (Belgium).

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Authors and Affiliations

Authors

Contributions

Conceptualisation: RMM, AHD, GC, CO, PdP, and PAW. Data curation: AHD, RMM, and GC. Formal analysis: AHD, RMM, and GC. Funding acquisition: PAW. Investigation: AHD, RMM, GC, and PAW. Methodology: AHD, RMM, GC, and PAW. Project administration: PAW. Software: RMM, AHD, and GC. Supervision: PAW and PdP. Writing—original draft: RMM. Writing—review and editing: AHD, RMM, GC, CO, PdP, and PAW.

Corresponding author

Correspondence to P. A. Willems.

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Conflict of interests

The authors declare no competing or financial interests.

Additional information

Communicated by Jean-René Lacour.

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Mesquita, R.M., Dewolf, A.H., Catavitello, G. et al. The bouncing mechanism of running against hindering, or with aiding traction forces: a comparison with running on a slope. Eur J Appl Physiol 120, 1575–1589 (2020). https://doi.org/10.1007/s00421-020-04379-5

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