An ideal treadmill?

We’ve recently been measuring the oxygen cost of walking in a group of amputees. The measurements we’ve made seem too good to be true. When we compare our results with those in the literature our amputees appear to be using considerably less oxygen to walk for a given distance. The differences are so substantial that I’ve asked our research fellow to look for possible explanations and one of the differences with those other studies is that we are making measurements with people walking overground whereas all the other studies have examined treadmill walking. This raises the old chestnut as to whether treadmill and overground walking can be considered equivalent or not.

In a sense the answer to this question has been known since 1632. In his Dialogue Concerning the Two Chief World Systems, Galileo Galilei proposed the hypothesis that has since become known as the principle of Galilean relativity that:

any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments

He illustrated this with a thought experiment based on a ship, in the modern world I think the example of a railway carriage is more appropriate. The hypothesis states that if you are in a sealed railway carriage then there is no physical experiment you can perform that will allow you to know whether you are stationary or travelling at constant speed (or the speed at which you are travelling). If, for example, you drop a weight, it will always fall vertically (as you observe it). Galileo stated this as a hypothesis, Newton went a little further and stated it as a principle, Einstein went even further and used this thought experiment for his theory of general relativity. Many experimentalists over the years have sought to disprove it, all have failed (except for those conducting experiments at near the speed of light).

Given that the body acts as a physical system (at least as far as the biomechanics of walking is concerned) we can use this principal to explore treadmill walking. Consider walking up and down that sealed railway carriage. There is no way you can know what speed the train is travelling from how it feels to walk. If you put an oxygen mask on and always walk at the same speed within the carriage you will always make the same measurement (or would if Oxygen consumption measurements were at all reliable!). Now assume that the train is travelling backwards at a speed that is identical to that at which you are walking forwards. Again we can argue that you will be consuming exactly the same amount of oxygen as you would if the train were stationary. From the perspective of someone watching from outside the train however you are walking on the spot. This is effectively a treadmill, a highly impractical treadmill, but a treadmill none the less. Under these circumstances it is clear that the oxygen consumption (or any other biomechanical variable) will be the same as for ordinary overground walking. I’ll refer to this as the ideal treadmill and reiterate that we can use one of the most widely accepted principles in the whole of physics to state quite categorically that walking on an ideal treadmill is biomechanically identical to walking overground.

I don’t go to the gym, I much prefer to run through the Cheshire countryside close to my home if I want some exercise, but those who do tell me that running on a treadmill is quite different to running overground. I think most people feel it is harder to run on a treadmill). Is this proof that Gailieo, Newton and Einstein and every other physicist who has ever tested this hypothesis are wrong – of course not. What it shows is that the treadmills are not ideal as I’ve defined it above. The important feature is that the belt does not continue to move at constant speed. When you land on the belt you exert a forwards direct force on the treadmill that tends to slow the belt down and when you push off you exert a force in the other direction that tends to speed the belt up. You are running on a non-ideal treadmill.

This has important implications for research because how much the belt varies in speed as you run on it will depend on all sorts of characteristics of the treadmill – whether the belt itself can stretch, the characteristics of the motor, whether there is any control system to help regulate speed. We can’t just assume that all treadmills are the same from a biomechanical point of view. Some I would guess, may be quite close to ideal, some, it is obvious, are very far from ideal. Many researchers have published papers comparing treadmill with overground walking but I don’t know of any of them that make the specific point that the results are valid only for the treadmill that they have chosen to perform the experiments on and should not be applied to treadmills in general. Following on from this we should not compare results from different papers on treadmill walking unless we have good reason to believe that the treadmills are equivalent.

One way of protecting against this might be to use comparative measures. We could, for example, report energy cost for amputees as a percentage of that for able-bodied controls walking on the same treadmill. This relative measure may be less dependent on the type of treadmill than the absolute measures. We’ve measured such controls in overground walking and can identify one study from another centre with equivalent data for treadmill based walking. Interestingly the differences are almost as large in the relative measures as in the absolute measures. There could be many reasons for this but one might be that the amputees and able-bodied cohort respond differently to the non-ideal nature of the treadmill. Thus an able-bodied person with intact musculo-skeletal anatomy and full proprioception might be able to adapt more easily to non-ideal treadmill walking than an amputee. As with all other measures this difference may be specific to the particular treadmill and it is dangerous to assume that this as a result applicable to walking on treadmills in general.

In summary the laws of physics dictate that the biomechanics of walking on an ideal treadmill (on in which the belt speed is constant) are the same as the biomechanics of overground walking. Any differences in biomechanical measurements between overground and treadmill walking must thus represent deviations from ideal behaviour (I’m a biomechanist so I’ll completely ignore the possibility of any perceptual or other psychologicl effects of course!) and it is likely that these vary from treadmill to treadmill. It would be interesting to know if anyone has compared results from different treadmills to investigate how significant this effect is.

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3 comments

  1. Very thought-provoking, especially as treadmill tests are so often treated as equivalent to overground tests. It would be interesting to see how different treadmill parameters – i.e. belt speed regulation, walking surface hardness, etc would influence the biomechanics profile in comparison to overground walking.
    Also, just curious – for the oxygen consumption testing did the treadmill studies that you are comparing to use a set speed or self selected walking speed?

  2. “I think most people feel it is harder to run on a treadmill” — definitely not in my experience! It feels almost like jogging on the spot; much easier. That’s the primary importance of upping the inclination a degree or two to match the difficulty. I suspect you’re right that the deformation of the drive system, etc., contributes to this in that there’s less “braking” (negative) force on the body as the forefoot makes contact as if it were landing on solid ground.

    1. Yes, thanks for this. One other person here at the University has also made exactly the same point to me and I think your explanation is spot on.

      My background is in clinical gait analysis so I don’t tend to think immediately fo running and other sporting activities. This makes things even more complex in that the effect of treadmills on walking may well depend on the activity being studied.

      A final issue is that in overground running air resistance is likely to become a more and more important factor the faster you run which is absent on a treadmill. I’m not sure at what sorts of speeds this will happen. Certainly in cycling air resistance makes a considerable contribution to the energetics of movement.

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