A bit of a work out

While still reflecting on the way we use terminology so misleadingly within gait analysis it might be worth thinking a little about the concept of external work. It’s a concept that is even older than I am. Although previous workers (notably Fenn and Elftman) had used similar concepts it was Giovanni Cavagna who popularised it with his classic paper from 1963.  (Cavagna et al. 1963). The article starts with the sentence, “The work performed in walking can be considered as being made of two components, the internal work and the external work”. My response to this is that you can consider it like that if you want but you are likely to confuse people if you do!

Graphs from Cavagna's 1963 paper showing how horizontal components of speed and displacement are calculated from acceleration data. Note that his data was taken from an accelerometer worn on the body whereas it is more common these days for similar techniques to be used based on forde plate measurements.

Graphs from Cavagna’s 1963 paper showing how horizontal components of speed and displacement are calculated from acceleration data. Note that his data was taken from an accelerometer worn on the body whereas it is more common these days for similar techniques to be used based on force plate measurements.

Let’s be clear that there is no external work in walking. All the work required for walking is generated internally by the muscles. The result of muscles (and ligaments) exerting forces on the skeleton is that the foot exerts a force against the floor and generates the ground reaction (following Newton’s third law) but the ground reaction itself doesn’t do any work. It can’t. In order for a force to do work the point of application needs to move and the ground doesn’t move (well, not very often).

Whether its name is correct of not, the concept is important because it allows an estimate of the energy cost of walking on the basis of force plate measurements alone (cuts out all that nasty kinematics). The theory behind the calculations is generally presented as  straightforward but actually requires some quite subtle reasoning.

Although the ground reaction doesn’t do any work, it is a force applied externally to the body and will result in the centre of mass of the body being accelerated (Newton’s first law). If we measure the ground reaction we can thus calculate this acceleration and thus how the centre of mass is moving (its velocity and displacement).

Now if we wanted to move an equivalent mass through the same trajectory we could do so by applying an external force of the same magnitude and direction as the ground reaction directly to its centre of mass. If we did this then the point of application of this imaginary force would move and it would do work. Knowing the laws of physics it is reasonably easy to calculate what this work would be.

This can be taken as equivalent to the work that the muscles have to do to move the centre of mass, but it should be emphasized that the external force applied at the centre of mass is entirely imaginary, for the purposes of the calculation only. All the work is done internally by the muscles.

Of course this is one of those areas where people who understand the underlying concepts can cope with the fact that the name is wrong and get on with life … but I suspect that the terminology has the potential to be extremely misleading for those who don’t.

Additional note. It may also be worth being explicit that the muscles do other things as well as moving the centre of mass. They also move the segments with respect to the centre of mass and the work required to do this is not captured in the calculation outlined above. The calculation will thus always be an under estimate of the true mechanical cost of walking. It’s interesting that despite the extent to which these techniques have been used there have been very few studies of how much of an under-estimate, either for normal walking or for walking with pathology of different kinds.



  1. Great post! One of the best descriptions I’ve seen to make the topic accessible.

    I fully agree that the term “external work” is confusing and often misleading. The definition used by Fenn was not the same as the definition used by Cavagna, adding to the confusion in prior literature. To expound slightly… Classically, Fenn (1930) used internal work to refer to that performed internally within muscle and liberated as heat, and external work to refer to the work performed by shortening muscle on the environment external to the muscle (i.e., on the body). Cavagna (1963) used the same terms (internal and external) differently, using internal work for work performed to move the body segments relative to the body’s center-of-mass, and external work for that performed to move the center-of-mass relative to the ground. Thus Cavagna’s internal and external work terms are both included within Fenn’s external work term. Cavagna’s terms are not only inconsistent with Fenn’s, but also confusing in their own right: Cavagna’s internal and external work are both performed internally within the body (mostly by muscle), even though no work is performed on the external environment (i.e., outside the body, assuming no ground deformation) during locomotion.

    I would advocate that the term “external work” be completely avoided in future publication/discussion, and that Center-Of-Mass work (or work performed on the body’s Center-Of-Mass) be used instead. Similarly, using terminology such as “Peripheral” to refer to contributions relative to the Center-Of-Mass seems less confusing/misleading than the term “internal.” When presenting results in publications it is always my preference to capitalize these terms and then define them mathematically, to avoid any ambiguity. Andy Ruina also has a nice rant (his words) on the topic of internal and external work which is available online (http://www.ruina.tam.cornell.edu/research/topics/miscellaneous/RuinaExternalWorkRant.pdf). It is primarily an analytical derivation going back to first principles.

    With respect to terminology, there is an added layer of complexity related to which terms should be called mechanical “work” vs. “energy change,” in order to be consistent with classical dynamics definitions. For instance, experimentally our Peripheral estimates are obtained from tracking segmental motion (without any explicit measurement of force), and therefore it is more accurate to refer to them as Peripheral energy change (rather than Peripheral work, which would be computed from a force multiplied by a displacement).

    We published a recent study that quantified both Center-Of-Mass and Peripheral kinetics during walking, and we discussed at length the rationale for each naming convention (Zelik, Takahashi and Sawicki 2015 JEB). This was also the first study to directly link Center-of-Mass and Peripheral energy changes with joint- and segment-level work sources – essentially to show that energy changes of and about the body’s Center-Of-Mass during walking could be fully explained by work performed about the hip, knee and ankle and in the foot segment (at least for positive work generation). The story is slightly more complicated for phases of negative work (e.g., during leading limb loading immediately after foot contact in walking) due to energy dissipated in soft tissues, which does not show up in inverse-dynamics joint work calculations. This soft tissue topic is discussed in more detail in some of our previous articles ( Zelik &amp Kuo 2010 JEB, ; Zelik &amp Kuo 2012 PLoS One).

    Thanks again for the broaching this topic, which continues to elicit substantial confusion amongst researchers and clinicians. I hope to see less and less of the term “external work” in future publications.

  2. Thanks, Karl, I must admit that I’ve got copies of Fenn’s papers but hadn’t read them in the detail that you have and certainly hadn’t noticed that he’d got a different definition of internal and external work.

    I’m also fascinated to see Andy’s “rant”.

    I’m glad you’ve reminded me of this post because I think I always intended a follow-up post extending this discussion to the calculation to the positive and negative “external” work done separately by different legs. I really don’t think this is valid. I’ve not got time to write this tonight though – maybe next week.


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