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Bioenergetics and biomechanics of cycling: the role of ‘internal work’

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Abstract

The ‘dissection’ of energy expenditure of cycling into the metabolic equivalent of the different forms of mechanical work done, inaugurated 30 years ago by di Prampero and collaborators, has been much debated in the last few decades. The mechanical internal work, particularly, which is currently associated to the movement of the lower limbs, has been approached, estimated and discussed in several different ways and there is no agreed consensus on its role in cycling. This paper, through re-processing previously published data of oxygen consumption during pedalling at different frequency, external load and limb mass, proposes a model equation and a multiple non-linear regression as the method to assess the internal work of cycling. With that tool a very consistent metabolic equivalent of the internal work is obtained. However, a software simulation of pedalling limbs showed, as suggested in the literature, that the link with the chain ring allows the system to passively revolve forever, after an initial push. This result challenges the very existence of the ‘kinematic internal work’ of cycling. We conclude and suggest that the ‘viscous internal work’, an often neglected and almost unmeasurable portion of the internal work that could be proportional to the ‘kinematic’ form, is responsible for the extra metabolic expenditure as measured when the pedalling frequency of cycling increases.

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Abbreviations

BCOM:

Body centre of mass

E :

Metabolic expenditure

eff:

Overall efficiency

effLL :

Overall efficiency of the loaded limbs condition

effUL :

Overall efficiency of the unloaded limbs condition

fr:

Pedalling frequency (Hz)

k :

Compound term accounting for limb rotational inertia (J kg−1 Hz−2)

k UL :

Unloaded limb inertia (J kg−1 Hz−2)

k LL :

Loaded limb inertia (J kg−1 Hz−2)

m :

Mass of the limbs (kg)

m%:

Lower limbs mass as a fraction of body mass

\( \dot{V}_{{O_{2} }} \) :

Metabolic work rate (W)

W ‘BIKE’ :

Mechanical work to overcome air drag, rolling resistance and drive chain and gearing energy dissipation

W D :

Mechanical work to overcome passive and ‘active’ air drag

W EXT :

The sum of W D and W R

W EXT* :

Mechanical work to move the centre of mass of the limbs

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

Mechanical external work rate as imposed by a cyclo-ergometer (W)

WINT :

Mechanical work to accelerate the limbs during the pedalling cycle

\( W_{\text{INT}}^{*} \) :

‘expected’ kinetic internal work in cycling (J)

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

‘expected’ kinetic internal work rate (W)

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

‘expected’ kinetic internal cost (J kg−1 m−1)

W OTHER :

Mechanical work of deformation of pedals during the push

W PROPULSOR :

Mechanical work to move the biological propulsive machinery

W R :

Mechanical work to overcome rolling resistance and drive chain and gearing energy dissipation

W TOT :

Mechanical total work needed to ride a bicycle

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Acknowledgments

Part of this work was presented as an oral presentation at the IV World Congress of Biomechanics in Calgary, 2002. I am particularly in debt with Jesus Dapena and Andy Ruina for the very helpful conversation we had in that occasion, when they suggested that the kinematic internal work of cycling could not exist at all.

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Authors and Affiliations

  1. Physiomechanics Laboratory, Department of Human Physiology, Faculty of Medicine, University of Milan, Via Mangiagalli 32, 20133, Milan, Italy

    Alberto E. Minetti

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  1. Alberto E. Minetti
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Correspondence to Alberto E. Minetti.

Additional information

Communicated by Susan Ward.

This article is published as part of the Special Issue dedicated to Pietro di Prampero, formerly Editor-in-Chief of EJAP.

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Minetti, A.E. Bioenergetics and biomechanics of cycling: the role of ‘internal work’. Eur J Appl Physiol 111, 323–329 (2011). https://doi.org/10.1007/s00421-010-1434-6

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