# How do we decide whether to walk or run?

Imagine yourself walking on a treadmill that starts at a reasonable pace: say, two and a half miles per hour. Every two minutes, the treadmill increases its speed by 0.2 mph: 2.7 mph, 2.9 mph, 3.1 mph, and so on. If you’re in good physical condition, at some point — usually between about 3.0 and 4.5 mph — you’ll find it more comfortable to start running instead of walking. Different individuals have different thresholds based on their fitness level and other factors, but even taking these things into account, it’s difficult to explain exactly why people start running when they do. Do different people have different thresholds for pain?

Gregory Daniels and Karl Newell paid 12 physically fit college students to walk on a treadmill as it gradually increased in speed. To disguise the real purpose of the study, the students were fitted with fake oxygen consumption meters and cardiographs. They were told to walk, but to begin running as soon as it felt more comfortable. They also rated their physical exertion every two minutes by pointing to a numeric chart on the wall (remember, their mouths were covered with the oxygen consumption meters so they couldn’t talk).

But most importantly, the walkers were also sometimes asked to complete simple addition and subtraction problems. Every 10 seconds, a new tape-recorded problem and answer was played, and the walkers had to raise their right hand to indicate a correct answer and raise their left hand for an incorrect answer. They repeated the experiment four times: two times with no math problems, and once each with easy (single-digit) and hard (double-digit) math problems. Here are the results:

The students transitioned to running at a significantly higher speed (about 4.78 mph) when doing the math problems compared to when there were no math problems (about 4.58 mph). There was no significant difference between the hard math problems and the easy problems, even though the students rated the hard problems as significantly more difficult.

Now take a look at this graph showing the students’ perceived exertion ratings for the body core (lungs, heart):

There’s nothing in this graph to show why the students decided to start walking rather than running. They became more and more exerted as the rate increased — whether they were walking or running.

But now look at this graph, which charts perceived exertion of the extremities (arms, legs):

Now you can see that the exertion rating climbs sharply until the students transition from walking to running. Suddenly the rating flattens out. By shifting to running instead of walking, the students are able to stop the increase in their perception of exertion. But remember, this transition occurs at a faster treadmill speed for those doing the math problems. So doing math problems somehow distracts people from experiencing exertion, both in their extremities and in the body core. But transitioning from walking to running can only alleviate the exertion in the extremities, not the core.

One possible way the math distracts people is through cognitive load: some cognitive resources are required even to determine that we are getting exhausted. If we’re using those resources to do math problems instead of thinking about how much we’re exerting ourselves, we don’t notice the exertion quite so much.

So why is there no difference in the walk/run transition between easy and hard math problems? Perhaps the hard problems weren’t hard enough. Or perhaps we’re limited in our ability to be distracted from exertion. Only a new study with more difficult math problems would be able to answer that question.

Related: Words of encouragement and exercise

Daniels
, G., Newell, K.M. (2003). Attentional focus influences the walk-run transition in human locomotion. Biological Psychology, 63(2), 163-178. DOI: 10.1016/S0301-0511(03)00024-3

1. #1 Freiddie
April 1, 2008

I never really noticed that there was an actual “transition” speed between walking and running!

2. #2 William Zantzinger
April 1, 2008

A cognitive load that distracts you from focusing on physical discomfort… one of the reasons why listening to your iPod will help you run further and faster. (Quite aside from the ability that certain ‘power tunes’ have to spur you on).

3. #3 matt
April 1, 2008

I think this is one of the bases for complex group exercise classes: keep the brain busy with difficult choreography and the body will work that much harder.

Those graphs are a teensy bit iffy, though, especially the first. Cropping the Y axis to emphasise differences is not usually best practice.

4. #4 Duarte
April 1, 2008

normally the easiest explanation is the correct one… Has anybody consider that maybe they took more speed to start running when they were doing problems was because they were being forced to use they hands to choose the correct answer and that is probably easier to do while walking?

If they could sustain the speed of the treadmill maybe most of the students choose to walk to make it more comfortable to answer the questions.

and also I find it strange that there are no error bars on the graphs? the experiments where not duplicated?

very unscientific in my humble opinion

5. #5 bg
April 1, 2008

Thank goodness I don’t do math while I work out or I wouldn’t get a very good workout!

Sometimes I think researchers that do these sorts of experiments go *so* far out of their way to eliminate variables that they create a situation that is extremely far-removed from the behavior they are trying to study. I mean, honestly, who does math while they run or drive, or recite poetry while they measure distance with their feet. rotfl!!

6. #6 Mike
April 1, 2008

Interesting study. I feel it focused on too much breadth, and not enough depth, though. A walking/running point is one thing, and perceived exertion while doing math is another. I would have enjoyed more study and insight into the point where people begin running, considering different activity levels, body sizes, etc.

7. #7 Ras
April 2, 2008

Well, it was 1st of april at least.

8. #8 Jessy
April 2, 2008

I find this very interesting because when I run, I have a tendency to do math in my head. I usually calculate my speed or how much longer I need to run to finish my 10k.

I guess I’m only doing that so that I’m not feeling the pain.

Cool!

9. #9 Yuri
April 2, 2008

I do ðŸ™‚
Since being little I tried to occupy my mind with something else when I had to run long distances (gym classes/army service) just to distract my self from the pain, I usually resorted to math. I always considered it to be just a weird habit of mine but i guess theres some sense behind it after all…

10. #10 mdreyer
April 2, 2008

Jazzercise involves frequently changing choreography which is distracting, especially for a klutz like me…I feel as though, besides being distracting, learning to do something, or *even* two things at once has neuro benefits beyond the aerobic stuff. I know this is woo-ey but it does feel like by thinking about something and meeting a challenge, even trivial stuff like what to do with your right arm, you are learning… I wonder with regards to ipods and running, what the role of rhythm is. If speech in free verse or just dialog (a movie script without music) would be more efficacious than just music…of course, lots of variables there.

11. #11 Mike Fox
April 2, 2008

I wonder if this is related to the fact that when I run, even three or four steps, I become less rational, even angry. This effect lasts for a while (several minutes).

12. #12 Nomen Nescio
April 3, 2008

this fits well with intuition. people doing physical work have been distracting themselves from the effort for centuries; sailing-ship sailors with sea shanties, soldiers on the march with cadences. this seems to indicate that math works, too, and gives a first clue as to how well it works.

in fact, my personal guess would be that math probably works less well than working songs or rhyming chants, because those two actually help you keep rhythm and pace, whereas arithmetic wouldn’t.

(i’m another weirdo who likes to figure how much farther i have to walk, and how long it’s likely to take me, by doing math in my head as i hike. i’m seldom very accurate, but it’s something to do with my otherwise unoccupied brain, and apparently it helps me put in more effort, too. i still never run, that’s too strenuous — but i can out-walk most people i know.)

13. #13 torcant
April 3, 2008

Maybe the connection between higher transition speed and doing math is not distraciton from discomfort. Maybe running requires more attention than walking. Therefore people find it harder to answer math questions while running. So they postpone running as much as possible in order to more easily grasp the question and answer.

14. #14 mainsequences
April 3, 2008

Different forms of gait (in humans, mainly walking and running, in quadrupeds, mainly, walking, trotting, galloping, etc) are qualitatively different. For example, in humans, walking is very efficient because our legs are mostly acting as pendulums, with much of the energy for each leg swing coming from gravity. In running, more muscular effort is required but there is also a big boost from energy elastically stored in the ligaments which gives a ‘bounce’ to each stride.

The decision to switch from one form of gait to another is therefore not really a cognitive one but is largely determined by boring dynamics. Gait transitions happen at characteristic Froude numbers. The dimensionless Froude number originally arose in naval architecture, but the form applied to gait is simply v^2/gl, where v is velocity, g is gravitational acceleration, and l is leg length.

For humans, optimal walking is at Fr ~ 0.25 (for an average sized person, about 1.5 m/s), the transition to walking occurs at ~0.5 (for an average sized person, about 2.0 m/s, corresponding well to the first graph above), and the physical limit of walking is ~1.0. You simply can’t walk faster than that.

As can be seen in the first graph (with, as noted, a deceptively scaled y axis to maximise the impression of an effect) any influence of cognitive load is small compared to the predicted transition speed.

The cool thing about Froude numbers is that they:
* apply across species (transitions occur for horses at the same values as they do for humans). The gait of kittens and rhinos obey the same forms.
* take account of different gravitational environments. Remember how Apollo astronauts kind of skipped rather than walked? That was more efficient for that velocity of movement than it would be on earth.
* can be used to infer dinosaur gait from static evidence such as fossil skeletons and series of footprints.

A good intro to this is Vaughan & O’Malley (2004), “Froude and the contribution of naval architecture to our understanding of bipedal locomotion’, Gait & Posture.

I’m not denying that there might be some cognitive load effect going on, but it is a minor factor compared to the physical dynamics of the body (supported by there being no effect of the degree of difficulty of the maths problems).

Cheers

15. #15 bgf
April 6, 2008

I find all this about Froude numbers to be very interesting. I notice the article didn’t really go into why the transitions occur where they do. I was curious about why, and the Froude numbers seem to make sense.

However small the cognitive effect is, though, I think it is clear that it is present (at least in this study). With no math problem, people transitioned to running at around 2.05 m/s, but with math problems, people transitioned at around 2.15 m/s. This seems to point to an effect from the cognitive effort.

So, while the transition speed may be for the most part based on the dynamics, there is some amount of conscious or sub-conscious input from the individual. I find this particularly interesting as another way that people can influence their actions beyond the role of physics.

16. #16 Scott
April 7, 2008

I use a GPS watch while running, and check every few hundred meters what my pace is. I often get mentally distracted by doing calculations such as “If I were to run this pace for 10k, what would my time be?” or “What how many seconds/mile do I need to speed up in order to finish in a certain time?”
Whenever I drift back from these distractions and check my GPS watch, my pace has picked up, though my effort hasn’t.

17. #17 Sybil
April 11, 2008

I think, this why the hick-ups stop when drinking five sips of water. The pain of hick-ups releases as soon as thoughts focus on counting. Concentration shifts from pain to counting and drinking five sips.

18. #18 penguindreams
April 16, 2008

The cognitive science side, I don’t know, but I’m a runner (and scientist, but in completely unrelated area). Some thoughts from that side:

* the difference (0.1 m/s) is right at the limit of the experiment’s resolution (the 0.2 mph increase), and the population is small. It’d be a help, probably, to get hold of a running club (so as to have a population that could easily walk then run for, say, an hour) and redo the experiment with 0.1 mph increments (the usual increment limit for treadmills)

* If the people were physically fit, but not accustomed to running, I’m afraid that the running side (later in the sequence) is being affected by their inexperience in running. Experienced bikers in excellent shape — for biking — when they first turn to running perform at a much lower level than you’d expect from their biking condition. (And vice versa — specificity matters to performance.) Tim Noakes, in Lore of Running, 3rd edition (and, presumably, 4th too but I haven’t gotten to that chapter yet) discusses some of this.

* The perception of effort is skewed by whether the subjects are experienced walker/runners. The energetic cost of walking increases fairly rapidly as you exceed the optimal pace (proportional to sqrt(leg length); there’s a nice paper in Nature a few years ago about run/walk transition as a function of gravity). The perception of this fact can be obscured in people who aren’t that attuned/experienced in the effort levels of their running and walking.

** This fact also suggests that the cognitive challenge could be made arbitrarily difficult and not change the transition speed further. My optimum walking speed is right on 16 min/mile (3.75 mph). I know the difference between that and 15 min/mile (4.0 mph) but can see that a distraction could keep me in my current mode to 15 min/mile. But there’s no way I won’t notice the elevation of effort going to 4.2 mph (14:15 min/mile) (I might keep walking anyhow, as I find it hard to run that slowly.). Go to 4.4 mph (13:40 min/mile) and most people won’t walk that fast without having trained for it.

* Perception of effort is also being skewed by the fact that the experiment was going solely from slower to faster as time progressed. Even at a constant pace, the perceived effort increases with time.

* Not sure if the Nature article mentioned this, or it’s in Noakes, or just common experience: While the energetic cost of walking increases rapidly with pace as you exceed the optimum, the converse is not true as you slow down from the optimum (efficient) running pace.

** I’ll suggest an alteration in the protocol: Start out at a comfortable, to the subject, running pace. For me, say 6.3 mph. Then start decreasing the speed by 0.1 mph and proceed as before with the math and perceived effort questions. Since the changes in efficiency are less from this side, there’s more chance for the cognitive effects, if any, to make themselves felt. And more chance to see a progression of effect on transition speed from harder problems. I can envision that, from this side, my transition point could be anywhere from 5.0 mph to 3.8 mph.

** Different protocol: People tend to stay in whatever mode they’re in, whether walking or running, even if other things are equal. Consequently, moving the speeds back and forth, repeatedly, across a range around the transition speed should show a rather mobile transition speed with a chance for progressive cognitive effects to be discerned.

While the experiment’s results are intuitively reasonable to me, I’m afraid that it didn’t (at least in the description here) address enough of the physiological side for me to be confident that it actually made a case to support that intuition.