temporal & spatial parameters

Walking in the groove

While I surfing the web doing a bit of background reading for last week’s post I came across this graph.

Ralston HJ (1958) Energy-speed relation and optimal speed during level walking. Int Z angew. Physiol. einschl. Arbeitsphysiol. 17 (8): 273-288.

Ralston HJ (1958) Energy-speed relation and optimal speed during level walking. Int Z angew. Physiol. einschl. Arbeitsphysiol. 17 (8): 273-288.

It’s another of the classic outputs of Verne Inman’s group, from Henry Ralston, and shows data for a healthy subject to support his hypothesis that we select our walking speed to minimise the energy cost of walking (the energy used to travel a certain distance). The hypothesis is so plausible that it has been almost universally accepted.

What interests me is that despite being so widely accepted I’ve never seen any suggestion of the mechanism through which we might achieve this. It’s a fairly basic principle of control theory that if we want to minimise any particular variable (such as distance walked for a given amount of energy) we need some way of measuring it. Thus it is very difficult to drive a car fuel efficiently if you just have a speedometer and a standard fuel gauge. If you add a readout to the dashboard telling you how much fuel you are using per kilometre travelled and the task becomes trivial. They should be compulsory in a fuel challenged world!

I’m not aware of any proprioceptive mechanism that would allow the brain to “know” how much energy it is using per unit distance walked. I can see that there are complex mechanisms regulating cardiac and pulmonary rate based primarily on carbon dioxide concentration in the blood which might allow us to sense how much energy we are using per unit time, but how can we possible sense how much energy we are using per unit distance. I’m not saying it’s impossible – the brain is a marvellous organ and it is possible that it integrates such a measure of energy rate (per unit time) with information about cadence and proprioception of joint angle and in order to derive a measure of energy cost (per unit distance). This is a complex mechanism however and certainly suggests that, as with so much in biology, whilst the basic hypothesis is extremely simple the mechanisms required to achieve this is far more complex than we might have imagined. As Ralston himself put it, “one of the most interesting problems in physiology is to elucidate the built in mechanism by which a person tends to adopt an optimum walking velocity such that energy expenditure per unit distance is a minimum”.

But this also makes me want to question the underlying hypothesis. Going back to the original paper (which you can read here), Ralston only produces data from one healthy subject and one amputee to support his hypothesis. I’m not aware of many others having explored the hypothesis on an individual level (the conclusion that the self-selected walking speed is close to speed of minimum energy cost for a sample does not mean that the relationship holds for individuals within that sample). I’d be interested to hear from readers of papers that have investigated this relationship in more detail.

The other point that Ralston made which is almost always overlooked is that the curve is “almost flat”. The curve only looks so steep because it has been plotted over such a wide range of values (from 0 through to 150m/s). Just looking at the data plotted I’d suggest that the speed can range from about  56 to 84 m/min whilst the energy cost remains within 5% of the minimum energy cost value. This is almost certainly within the range of measurement error for a variable such as energy cost. In other words the really remarkable thing about the energy curve is that it allows us to walk over quite a range of speeds without having a measureable effect on our energy cost. It is interesting that Ralston managed to make this point and suggest that we select walking speed to minimise energy cost in the same paper!


What is normal walking?

In the last post I commented on the recent paper by Dall et al. (2013) and the context of its publication. As commented on by the author in response to that post, some of the results are interesting in their own right. (I was going to paste a couple of figures from the paper into this article but the publishers require a payment of over $300 to do this legally so you’ll have to download a copy of the paper yourself if you want to see the evidence.)

Figure 1 shows the frequency distribution of minute epochs during which walking was recorded at various cadences. The mean cadence was 76 steps per minute with a cadence of less than 100 steps per minute in about 80% of the minutes during which any walking was recorded. When healthy adults walk at “self-selected” speed in the gait lab they tend to walk at cadences of well over 100 steps per minute (A brief review of the previous literature in Winter (1991) suggests values between 100 and 120). We can thus see that cadence in everyday activity is very different to that during walking in the laboratory.

The paper also includes a second graph (Figure 4) showing the same data but for the sub-set of minutes when the participants walked for the full minute. This shows a mean value of 109 (±9) steps per minute which is in much better agreement with the self-selected walking speeds recorded in the laboratory. The most obvious explanation of these two graphs together is that when we walk for short bouts we do so at much slower cadences than we tend to look at in the laboratory but when we walk continuously for a minute or more that we appear to walk at similar speeds (although the graphs tends to suggest that there is more variability in this in real life than I’d expect in the laboratory).

This can be put together with the data from Orendurff et al. (2008) that shows that 90% of bouts of walking are for less than 100 steps and 75% are less than 40 steps to suggest that the walking we investigate in the gait laboratory is quite different to the walking the we use most frequently in our everyday lives. This worries some people but this misses the reason for performing clinical gait analysis as we do. We use level walking at self-selected speed because it is a well-defined stereotypical movement that we understand reasonably well. We hope that analysing it will give clinical insights into impairments of neurological, muscular or skeletal function. The ultimate hope is that if we base treatment on the results of this analysis then we will improve function in “laboratory walking” and in every day walking as well. I hope you can see that this line of reasoning does not necessarily require laboratory walking to be representative of everyday walking.


Dall, P. M., McCrorie, P. R., Granat, M. H., & Stansfield, B. W. (2013). Step Accumulation per Minute Epoch Is Not the Same as Cadence for Free-Living Adults. Med Sci Sports Exerc.

Orendurff, M. S., Schoen, J. A., Bernatz, G. C., Segal, A. D., & Klute, G. K. (2008). How humans walk: bout duration, steps per bout, and rest duration. J Rehabil Res Dev, 45(7), 1077-1089.

Winter, D. (1991). The biomechanics and motor control of human gait: Normal, Elderly and Pathological (2nd ed.). Waterloo:: Waterloo Biomechanics.