Work done running on an inclined treadmill

[Grinkle]

At this point, I think that we are all on the same page and are preaching to the choir.

Agreed.

Moving the discussion what is the simplest way to look at it, I claim that the work being done is most easily calculated by looking at the torque vs radial displacement of the treadmill motor. This motor is moving the runners center of mass down the belt as the runner moves themself back up the belt. The motor does work in preventing the belt from slipping.

Many people simply don't think this is the case - they have never seen a person too heavy for a given treadmill try to run on an underpowered treadmill. The belt slips and they fall forward as their feet move backward out from under them. Like @russ_watters said, it becomes trying to run on ice.

In these discussions, I tend to get very tied up in the runner's biomechanics for which the kinetmatics are very complex, but the kinematics of the treadmill motor are very simple. Neglecting heat dissipation in the friction of the treadmill (not trivial for most treadmills I suppose), the motor work must be the runners work.

 

[Roger Chase]

Awesome discussion! I work in the exercise equipment industry as a test engineer with a physics background and this topic comes up regularly for various pieces of equipment, one of which is the TM. The human body is actually pretty complex mechanically and we do see some surprising results sometimes...if you examine the current wave forms going into the drive motor when a person is on a TM (we call this an active load) it drops with every footstep by quite a bit because the person is actually pushing the walk belt back which "assists" the drive motor temporarily. I tried to dig through some of the O-Scope captures we did in previous testing for TMs and the one below seemed pretty cool. This is at 0° incline for demonstration purposes. The Yellow waveform is the brushed DC motor current, Blue (which is kind of obscured in the background) is the PWM'ed motor voltage and the Red is their product (power in Watts). On an incline this effect is amplified because you have more mechanical advantage i.e. it's easier to push the belt since you're trying to keep upright and because the normal force mgCosθ is less since θ>0 so the peak current is less because overall friction is less and the dips are more pronounced. I'll see if I can find some comparative incline/non-incline examples or actually it might take less time if I just went out to the lab and took new data...I could use the exercise anyways :)

 

[jbriggs444]

Agreed.

Moving the discussion what is the simplest way to look at it, I claim that the work being done is most easily calculated by looking at the torque vs radial displacement of the treadmill motor. This motor is moving the runners center of mass down the belt as the runner moves themself back up the belt. The motor does work in preventing the belt from slipping.

The motor absorbs work in preventing the belt from slipping.

Neglecting heat dissipation in the friction of the treadmill (not trivial for most treadmills I suppose), the motor work must be the runners work.

The motor's work must be the additive inverse of the runner's work [ignoring frictional losses].

 

[rude man]

I've thought about this for a long time and discussed it with a professor of mechanical engineering. We both say the apparent gain in height on a treadmill is far greater than that of climbing an actual mountain. PeroK seemd to have the most credible answer. I wil probably continue to mull over it for some time yet.

 

[A.T.]

We both say the apparent gain in height on a treadmill is far greater than that of climbing an actual mountain.

What is "apparent gain in height", and why is it relevant?

 

[A.T.]

The Yellow waveform is the brushed DC motor current, Blue (which is kind of obscured in the background) is the PWM'ed motor voltage and the Red is their product (power in Watts).View attachment 212748

The crucial parameter would the speed of the belt. If there is only negligible variation of belt speed, you can define an inertial frame where the support surface is at rest. Per Galilean Invariance this frame is equivalent to the rest frame of a hill incline (ignoring air drag). So there is no physical reason to walk differently and do different work, just psychological ones.

 

[lesaid]

I wonder if a major contributor to the perceived greater effort required to climb a hill is simply down to the rough ground. I know personally, it takes substantially more effort to hike up a rough, uneven slope than a smooth steady gradient, and found a treadmill easier. On smoother surfaces, it is natural to fall into a regular rhythmical gait which (presumably) is more efficient that the constant, step-by-step adjustments required when going up a real hill.

When on a treadmill, there is also the temptation to rest one's hands on the rail - while serious users presumably may not do this - doing that could help a lot with maintaining balance, increasing the efficiency of the walking/running?

Has anyone compared the perception of running up a long steady incline on a road or tarmac path against a treadmill of similar slope? I'm guessing it may still seem harder due to psychological differences, but perhaps much less different? Perhaps hard to come up with a fair comparison with all the subjective influences at work!

 

[A.T.]

I know personally, it takes substantially more effort to hike up a rough, uneven slope than a smooth steady gradient, and found a treadmill easier.

Yes, of course. The equivalence is to a smooth constant slope hill.

When on a treadmill, there is also the temptation to rest one's hands on the rail - while serious users presumably may not do this - doing that could help a lot with maintaining balance, increasing the efficiency of the walking/running?

That can make it completely different, depending on how much force you put on the rails.

 

[Sherwood Botsford]

Consider this thought experiment:

I stand on the belt, and move backward dropping 10 cm.
I then take two steps forward rising 10 cm.

In this case I'm raising my center of mass (cm) each time. It should be the same as going up a real hill.

Now if I do the old calculus limits bit, and do smaller and smaller steps back and forward, what changes?

This gets messy because people don't roll forward, but bounce all over the place. As the steps decrease, I can keep my torso at a constant level, by extending my leg to make it longer. Force times distance. I'm not really climbing, but the grade is more than it would be if the treadmill were level. This would support the argument above that it's about half the effort.

consider another experiment: What about biking on a treadmill? This isolates the user part of the system (cyclist + bike) from the treadmill in a more tractable way. Does biking on a sloped treadmill take more energy than biking on a flat treadmill? Yes. The wheel meets the treadmill on an angle. This will produce a torque on the wheel trying to roll the cyclist backward. He has to overcome that torque in addition to the other work.

However he is not gaining potential energy.

Comments?

 

[Grinkle]

@Roger Chase Its really generous of you to go to the trouble to share that data. If you have a way to add the radial velocity of the motor shaft or the belt speed (they should be proportional I think so it doesn't matter much which you plot if one or the other is available) like @A.T. was saying, that would be interesting to look at.

If one can calibrate out the unloaded work a treadmill motor does and if the addition of a runner does not change the dynamic frictional losses in the system significantly, then a treadmill with instrumentation to record the motor currents / voltages should be able to report very precisely the effective work a runner is doing, similar to work computers on bicycles. I am curious to know if any treadmills do this, if happen to know. Not sure I can ask this on a runner forum without folks thinking I am asking about heart rate calorie burn computations.

 

[jbriggs444]

This would support the argument above that it's about half the effort.

What argument that what is half the effort of what?

 

[votingmachine]

I think the effort being ignored is the "ride" on a treadmill. Consider if you put one foot on the side rail, and move the other thru a walking motion. That foot mimics walking up a hill. But it is clearly not moving the body mass up a hill. You do lift your foot to move it up the treadmill. But then it just rides down. Moving two feet can seem to be that same motion. You lift your foot and move it up, then let it ride down, barely working to keep your mass centered. Then you lift the next foot and repeat.

When you walk up a real hill, you never get the "ride". You push thru the entire stroke. If you walk up a flight of 20 stairs, you use muscles the entire stroke. If you walk 20 steps on an escalator moving against you, you get opportunities to rest. You lift your foot a single stair height, but as you extend your leg, the stair moves down, rather than lifting your body up. If you move up one step on stairs, you are higher at the end. If you move one step on the escalator, you are the same height. It seems obvious that there was less work. I feel that I work harder, walking UP an UP escalator, and work less hard, walking UP a DOWN escalator,

When you stand in place, you are working, even though the physics says you are not. There is constant muscle use. Don't ignore the inefficiency of the human body as though it is a "body" at rest. It could be that the difference is just in inefficiencies.

 

[jbriggs444]

When you walk up a real hill, you never get the "ride".

You are going to have to make this argument more detailed. As it stands, it is not even wrong.

Let me see if I can fill in the blanks where the details should be.

You do lift your foot to move it up the treadmill. But then it just rides down

During the downstroke on a moving treadmill, your muscles are contracting and your leg is extending. The "just rides down" verbiage suggests that you believe that no effort is expended and no work is being done.

Please clarify.

Edit: found it.

It seems obvious that there was less work

The word obvious is the clue that this is the error.

 

[Grinkle]

Moving two feet can seem to be that same motion.

No, it is not that same motion.

If you are standing on an incline and you drag one foot backwards along the ground while your weight is supported by your other foot its not hard. If you start to walk up the incline, its hard.

If you are standing on a treadmill and you let one foot travel freely on the belt while supporting your weight on the other foot, its not hard. If you start to walk up the inclined belt with both feet, its hard.

 

[lesaid]

I stand on the belt, and move backward dropping 10 cm.
I then take two steps forward rising 10 cm.

Each time you are carried back and down, you lose potential energy, which ends up in the motor-drive assembly - either as a reduction in energy supplied to the motor, or as in heat from a brake, perhaps.

Each time you step up, you are regaining that potential energy, this time from the chemical energy reserves in your body, via the actions of your legs. If you step up the same distance as you were previously carried down, you end up with exactly the same amount of potential energy.

Over time, the net effect is to transfer energy from your body to the motor/drive system.

At least, that's my perception.

 

[votingmachine]

You are going to have to make this argument more detailed. As it stands, it is not even wrong.

Let me see if I can fill in the blanks where the details should be.

During the downstroke on a moving treadmill, your muscles are contracting and your leg is extending. The "just rides down" verbiage suggests that you believe that no effort is expended and no work is being done.

Please clarify.

Edit: found it.The word obvious is the clue that this is the error.

I should have used the word PERCEIVABLE, rather than obvious. I can add my voice to the chorus that says "it really is easier on a treadmill". How that difference in observed effort is reconciled with the physics of motion is not clear. I think it is partly in the "ride" effect.

People who have the experience of the two exercises know that the treadmill is not as much physical effort. That difference is real, even if the physics of the masses tells you that the same work is done on the system. Perhaps you need to calculate heat loss, which is not included in your mass-of-the-body calculation. I can say that the motion of my leg on the treadmill is perceptibly less effort than the motion of my leg on the ground. It may be that the explanation is entirely in the inefficiencies of physiology. Or balance differences between running between two guard-rails and running without them.

The temptation is to say that the effort has to be from a reduced work. You are clearly arguing that the work has to be the same, on an ideal treadmill, as on an ideal hill. That seems right, but I am still tempted to say that there is some work difference. It really does just seem more different than ordinary changes to gait and posture would account for.

 

[jbriggs444]

I think it is partly in the "ride" effect.

That effect appears to be a figment of the imagination. It has no basis in physical reality. There is no magical "I can stop running and let gravity do part of the work" mechanism in action.

 

[A.T.]

You are clearly arguing that the work has to be the same, on an ideal treadmill, as on an ideal hill.

With a human, nothing has to be the same. But there is no mechanical reason for it to be different.

 

[votingmachine]

That effect appears to be a figment of the imagination. It has no basis in physical reality. There is no magical "I can stop running and let gravity do part of the work" mechanism in action.

Yet when you run up a hill, you cannot separate the leg movement from the center of mass movement. On a treadmill you can. My movement is different. I think the legs that support my immobile upper body are moving in a way that is different from the way my legs move when they are forced to move my upper body up a hill.

The ideal movement on a treadmill would be to keep a transient support structure in place under the upper body. The ideal movement on a hill is to keep the upper body moving upward. Yes the treadmill is moving, and yes I use a running stride (more or less). But I think there is a difference in where the weight is, that does feel like I let the treadmill move my foot, rather than moving forward on the treadmill in a natural stride.

It could be a figment of my imagination. I might be imagining a different stride feel. I don't think I am though. I don't think I am calling upon anything magical. I am calling for a more complete description than the one that describes a 60 kg mass moved upwards 10 meters in a stationary frame, compared to the same 60 kg mass moved up 10 meters in a moving frame. Which you keep effectively saying is the same.

Where you make your mistake is in saying that therefore, any perception of a difference is a figment of imagination.

There are lots of differences between physics and physiology. I can bench press 60 kg 10 times. I can't bench press 600 kg once. The work is the same. The power differences matter to the individual. Sometimes incorrectly called work ... if I add a little weight, I struggle disproportionately and work harder. The effort and inefficiencies are getting tangled with the ideal work. Your rebuttal that it is a figment of imagination doesn't hold up to the reality of exercise.

 

[A.T.]

I am calling for a more complete description than the one that describes a 60 kg mass moved upwards 10 meters in a stationary frame, compared to the same 60 kg mass moved up 10 meters in a moving frame.

https://en.wikipedia.org/wiki/Galilean_invariance

 

[Grinkle]

Yet when you run up a hill, you cannot separate the leg movement from the center of mass movement. On a treadmill you can. My movement is different. I think the legs that support my immobile upper body are moving in a way that is different from the way my legs move when they are forced to move my upper body up a hill.

Your rebuttal that it is a figment of imagination doesn't hold up to the reality of exercise.

You are making this more of an either / or than it really is. Your running efficiency may be different on a treadmill than on a stationary surface. There are many reasons this may be the case. The physics of how gravity operates on mass that is on an inclined surface is NOT one of these reasons. Read post #65 by @A.T. Its a better / simpler visual than my post #63, I think. If you are inside such a box that moves at a fixed rate and you really don't want the back edge of the box to hit you, just like you don't want to fall off the back of a treadmill, your running efficiency may well change, but it won't be because gravity is now somehow behaving differently. Neither will your modified gait be a figment of your imagination. In fact, you couldn't tell if you were on a treadmill and the box were stationary or if you were on a long still belt and the box were moving. If you think you could tell the difference, explain how.

Your movement may be different. I think I run differently on a treadmill. I think its the pace-enforcement that changes my gait.

There are studies that show runners are less efficient on a treadmill than running outdoors, so it is not a universal conclusion that everyone find a treadmill easier than outdoors. I would say anecdotally most runners say the treadmill is easier, just noting that real studies don't bear that out. Here is one -

https://www.active.com/running/articles/equating-treadmill-and-outdoor-running?page=2

Snip:

Why is perceived effort higher, and performance consequently reduced, on the treadmill? Samuele Marcora, an exercise physiologist at the University of Kent who studies the relationship between perceived effort and endurance performance, says that running outdoors...

1. Produces more airflow against the body
2. Involves a visual perception of movement that is lacking indoors, and
3. Promotes more dissociative thinking through greater overall visual stimulation

All of these factors have been shown to reduce perceived effort.

 

[jbriggs444]

Yet when you run up a hill, you cannot separate the leg movement from the center of mass movement. On a treadmill you can.

That is not correct. You can separate leg movement from center of mass movement regardless. Stop and think.

Edit: You may be trying to suggest that how you move your center of mass depends on how you move your legs. That's true on both hillside and treadmill.

 

[russ_watters]

I should have used the word PERCEIVABLE, rather than obvious. I can add my voice to the chorus that says "it really is easier on a treadmill". How that difference in observed effort is reconciled with the physics of motion is not clear. I think it is partly in the "ride" effect.

Sorry, but this isn't correct.

The "ride" down is indeed free, but that is just what makes a treadmill a treadmill (keeps you stationary) and doesn't have any impact on the energy expenditure compared to walking up a hill. To see this more clearly, let's make the treadmill start and stop:

1. Treadmill is stationary and you take a step forward/upward. Then you stop.
2. Treadmill moves backwards to where you started and it stops.
--Repeat as desired.

It should be obvious that step 1 is exactly identical to walking up a hill -- because with the treadmill stopped it is just walking up a hill. Step 2 is the "free" (to you) ride down to reset for the next step.

 

[votingmachine]

Your movement may be different. I think I run differently on a treadmill. I think its the pace-enforcement that changes my gait.

There are studies that show runners are less efficient on a treadmill than running outdoors, so it is not a universal conclusion that everyone find a treadmill easier than outdoors. I would say anecdotally most runners say the treadmill is easier, just noting that real studies don't bear that out. Here is one -

https://www.active.com/running/articles/equating-treadmill-and-outdoor-running?page=2

Snip:

Why is perceived effort higher, and performance consequently reduced, on the treadmill? Samuele Marcora, an exercise physiologist at the University of Kent who studies the relationship between perceived effort and endurance performance, says that running outdoors...

1. Produces more airflow against the body
2. Involves a visual perception of movement that is lacking indoors, and
3. Promotes more dissociative thinking through greater overall visual stimulation

All of these factors have been shown to reduce perceived effort.

That link opens:

Given the fact that the energy cost of running on a treadmill is slightly lower than the energy cost of running outdoors, at least at faster speeds ...

I did not know that it was not universal. I thought everyone found a treadmill easier. That link says that runners perform better outside, even though it is harder. Perceived effort being inaccurate could be more important than actual differences in effort.

 

[votingmachine]

Here is a link I found that may more accurately portray what I feel as a "ride":
https://www.active.com/running/arti...gs-to-know-about-treadmill-training?cmp=23-69

Hamstrings: Because a machine powers the treadmill belt, the mechanics of your running stride differ when you run outside. When running on the treadmill, you use your quads to push off. But, unlike outdoor running, where you would typically rely on your hamstrings to finish the stride cycle and lift your leg behind you, the propulsion of the belt does much of that work for you. This means your hamstrings aren't firing as much and don't get worked running inside as they would outside.

Maybe it is that free finish to the stride cycle that feels like a ride.

 

[A.T.]

Here is a link I found that may more accurately portray what I feel as a "ride":
https://www.active.com/running/arti...gs-to-know-about-treadmill-training?cmp=23-69

Hamstrings: Because a machine powers the treadmill belt, the mechanics of your running stride differ when you run outside. When running on the treadmill, you use your quads to push off. But, unlike outdoor running, where you would typically rely on your hamstrings to finish the stride cycle and lift your leg behind you, the propulsion of the belt does much of that work for you. This means your hamstrings aren't firing as much and don't get worked running inside as they would outside.

Nonsense.

 

[Grinkle]

Perceived effort being inaccurate could be more important than actual differences in effort.

Especially when there are no actual differences in effort.

 

[votingmachine]

Nonsense.

Why is that nonsense? I see the same thing repeated in other links.

http://www.realclearscience.com/quick_and_clear_science/2017/05/30/you_may_need_to_run_15_faster_on_a_treadmill_to_equal_running_outside.html

In 1996, University of Brighton exercise scientists Jonathan Doust and Andrew Jones measured the energy use of nine trained male runners as they ran outdoors on a flat surface and on a treadmill. They found that running on a treadmill at consistent speeds between 6.7 and 11.1 miles per hour was less energetically demanding compared to running outside

...

researchers found that subjects exerted themselves to a greater extent on the track compared to the treadmill, despite running at the same speed.

...

As to why the treadmill was easier, the researchers speculated that the flimsy board of most treadmills upon which the belt runs could return elastic energy to the runner with every step, literally putting a spring in their stride.

I would think that the question is one amenable to study, and studies have indeed been done. The question appears to be incompletely answered. But that does not make it nonsense, but a physiological effect that is still poorly understood.

 

[A.T.]

Why is that nonsense?

The explanation of the difference ("because the belt is powered") is wrong, for the reasons stated many times in the thread.

I see the same thing repeated in other links.

http://www.realclearscience.com/quick_and_clear_science/2017/05/30/you_may_need_to_run_15_faster_on_a_treadmill_to_equal_running_outside.html
As to why the treadmill was easier, the researchers speculated that the flimsy board of most treadmills upon which the belt runs could return elastic energy to the runner with every step, literally putting a spring in their stride.

That is not the same explanation as the previous link. An elastic board is obviously not equivalent to a non-elastic road. Have you now moved from arguing about ideal treadmills to the imperfections of real ones?

 

[votingmachine]

The explanation of the difference ("because the belt is powered") is wrong, for the reasons stated many times in the thread.That is not the same explanation as the previous link. An elastic board is obviously not equivalent to a non-elastic road. Have you now moved from arguing about ideal treadmills to the imperfections of real ones?

No I have not. I'm not really interested in arguing at all. I was trying to add information about why treadmill running is WIDELY regarded (myself included) as easier.

The answer MUST be physiological, IF the physics of the two systems are the same. OR it lies in differences between the systems. OR there is no difference and the effect is entirely in the mind of runners. All of these are valid beginning hypothesis. If you want to argue with the researchers speculations, then contact them.

Treadmills seem easier. And researchers have seen a difference. I'm not sure why that difference exists, given that an ideal treadmill would be the same as an ideal track. The treadmill rubber definitely stretches on contact and release, and runners feel that, and change stride. The foot contact position was shown to be different in high speed video of treadmill and track runners and researchers have speculated about that. I think the foot release feels different, and again, that could again be the elasticity of the rubber (or spring in the platform) ... to me it feels like a free push on the back end of the stride.

The subject is interesting and far more complex than saying that there are two equivalent reference frames. Perhaps the elastic rubber stores and returns energy. Or the bouncy platform stores and releases energy. Or the gait differences matter. Certainly it is WELL understood that outdoor running has air resistance, and treadmill running has none.

If you are waiting for me to say that two ideal moving reference frames are the same physics ... I said that many posts ago. And I said there are perceived differences in effort. And I see research that says there is also a measurable difference in metabolic effort. So again, speculation about why is relevant. I did not read the "belt is powered" part carefully. More likely the "belt is elastic" is more relevant. Aid in finishing the stride cycle was the part I was calling attention to.

Be sure to recognize that running outdoors, you run against air resistance. And running on a treadmill, your body remains fixed relative to the air (very little air resistance). There are differences in the actual physics.