We asked Prof. Pietro Enrico di Prampero, a pioneer in metabolic analysis and a pillar of the gpexe scientific team, to answer a few questions about his latest paper, “Energy cost of running uphill as compared to running on the level with impeding horizontal forces.” His responses help clarify the study’s motivations, findings, and potential applications.
What was the key motivation behind comparing the energy cost of running uphill to running on flat terrain with horizontal impeding forces?
The energy cost of running at constant speed on flat terrain has been well known since the first half of the last century: it amounts to about 1 kcal per kg body mass and km distance.
Obviously enough, when running uphill or downhill, the corresponding energy cost increases/decreases as a function of the slope, the appropriate relationship being also well known. This is not the case for accelerated/decelerated running; indeed, the very short duration of these events does not allow an accurate assessment of the energy expenditure. This is a most unpleasant state of affairs because of the important role of acceleration in athletics (e.g. the 100 – 400 m sprints) as well as in team sports (e.g. soccer). However, during accelerated running of flat terrain, the subjects must lean forward so that the angle between his/her mean body axis and the terrain is smaller, the larger the acceleration. This state of affairs is equivalent to running uphill, in which case the angle between the mean body axis and the terrain is smaller, the steeper the slope (Figure 1).
Simple geometrical considerations show that the slope of the terrain with the horizontal (i.e. the tangent of the angle 90 – α in Figure 1) is equal to the tangent of the angle between g’ and g, i.e. to the ratio between the forward acceleration and the acceleration of gravity (af/g). Hence, once the acceleration is known, this ratio, defined for simplicity as Equivalent Slope (ES), can be easily obtained, and the corresponding energy cost estimated from the relationship between the energy cost of running uphill at a constant speed and the corresponding slope that, as mentioned above, is well known. This state of affairs applies equally well to deceleration and downhill running.
And what about the effect of a horizontal impeding force?
When running on flat terrain at constant speed against a horizontal impeding force the situation is equivalent to accelerated running on flat terrain wherein the impeding force plays the role of the acceleration; as a consequence, the ES is given by the ratio between the impeding force, per unit body mass, and the acceleration of gravity. The advantage of the “impeding force “approach is that, within a rather large range of forces, the experiments can be performed for a long enough time to achieve a steady state condition that, as is the case for running uphill, allows a direct estimate of the energy cost, which was not the case for the accelerated xrunning on flat terrain. The results of our study do show that the energy cost values estimated thanks to the “impeding force” approach, for a given ES, are rather close to those applying to uphill running at constant speed at the corresponding slope.
Can it be concluded that the three conditions are biomechanically equivalent?
Yes, for what has been said, accelerated running on flat terrain, running on flat terrain at constant speed against a horizontal impeding force, and running at constant speed uphill can be considered biomechanical equivalent.
In terms of energy expenditure, what did you find to be the main differences between running uphill and running with horizontal resistance?
The biomechanical equivalence described above between the three running conditions applies strictly to the mechanical work performed on the centre of mass of the subject. As such it is based on the implicit assumption that the mechanical efficiency of the transformation of metabolic into mechanical energy by the muscles, as well as the “internal work” (i.e. the work necessary to move the upper and lower limbs in respect to the centre of mass), are equal in all cases. The slight differences observed in our recent study between the cost of running at constant speed against an impeding force and the corresponding cost of uphill running suggest that this may not be entirely true. However, the data obtained so far suggest that the differences between the two conditions are not large. In any case, further studies dedicated to assessing in more detail stride frequencies and mechanical work (internal and external) in the three conditions described above are entirely warranted to obtain a more correct evaluation of the equivalence between accelerated running on flat terrain and running at constant speed uphill or downhill.
Interview with Professor Pietro Enrico di Prampero.