Stairmaster Physics: Exploring Exercise Value & Mechanics

[A.T.]

I never claimed that my speed 'relative to the ground' mattered.

Then how do you define the following?

... actually elevating...

Elevating in what frame of reference? Movement is frame dependent, and so is work.

Please read the other threads, before you keep repeating more wrong stuff that was already debunked there:
https://www.physicsforums.com/threads/fitness-treadmill-incline.937725/
https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/

 

[A.T.]

...will do less work

See post above.

 

[russ_watters]

Referencing the original question, I stand by my previous post (#10). Any one user may get more or less benefit than any other user based on the way they use the machine.

In other words, if you change your gait it might get more or less efficient. This is both obvious and pointless as pertains to this thread.

 

[russ_watters]

This is not correct.

Actually, it is true - with the caveat that it isn't very helpful to the thread, per my previous post...

Please note: the OP and the post quoted were about "exercise value", which is different than mechanical work. We've for the most part been assuming the motion is identical in the various cases, making the "exercise value" the same because the mechanical work done is the same.

But energy is *not* conserved in human motion. That means that smoother motions are more efficient than jerky motions because the extra acceleration energy of a jerky motion is not recovered when you decelerate again. So if you change your gait when using a machine you may expend more or less energy to do the same amount of mechanical work.

 

[Dullard]

I've pondered some more. I apologize for getting the thread locked - I was smiling when I typed the offending words, but that apparently didn't come across.Is a treadmill/stairmaster as much ‘exercise’ as an equivalent ramp/stairs? I still don’t think so.

Case 1 (Treadmill)

Imagine a wheeled cart on an inclined (moving) treadmill. Neglect friction, etc. The cart is attached to the uphill end of the treadmill structure with a fixed rope – the rope is parallel to the deck of the treadmill. The tension (T) in that rope is a function of the incline angle and the weight of the cart; it is (exactly)the force required to maintain the cart position. The force does not change if the treadmill is stopped. It doesn’t change if the treadmill is reversed.

Case 2 (Ramp)

Move this rig to a stationary ramp of the same incline (or stay on the stopped treadmill). Note that the tension in the rope is exactly the same as in Case 1. The cart isn’t going up the ramp. You’ll need to ‘tug’ on the rope to get the cart moving and reel in the rope to maintain motion. The tension in the rope will (initially) be higher than ‘T’ while the cart accelerates from rest to climbing velocity; call that difference ‘F’. Once at climbing velocity, you’re back to ‘T.’ The application of the additional force (F) over the distance where velocity is changing is work that is not required in Case 1.

It is tempting to say that this is not steady-state behavior, and should be neglected for this and any similar analysis. In the example of the cart, I agree – there is no steady-state difference between a treadmill and a ramp. In the case of human locomotion, I have an apparently irreconcilable problem:

Any actual experiment comparing the amount of exertion required to walk on a treadmill/stairmaster with the effort required on their geometrically equivalent low-tech counterparts empirically demonstrates that they are not equivalent in terms of effort (it isn’t even very close). I’ve done it, and don’t know of anyone (who actually did an experiment) who disagrees.

Unless my understanding of the experimental data is wrong, I can only conclude:

The nature of human locomotion (the complexity of many parts moving different directions) requires that the penalty (‘F,’ above) is paid (at least in part) at every new step.

I suspect that the reason that the simple models don’t accurately answer the basic question is the inability of a human to ‘benefit’ from negative work. ‘Effort’ isn’t paid back on the other side of the hill. Work which would sum to zero in an over-simple model leaves a user sweating.

 

[jbriggs444]

The nature of human locomotion (the complexity of many parts moving different directions) requires that the penalty (‘F,’ above) is paid (at least in part) at every new step.

You have not identified any difference in gait on the moving treadmill versus a stationary ramp that would be required to make F (the initial acceleration penalty) applicable.

 

[Dullard]

I don't believe that a difference in observable gait is required. The forces are different in the 2 cases, not (necessarily) the gait.

 

[A.T.]

In the example of the cart, I agree – there is no steady-state difference between a treadmill and a ramp.

So we agree that there is no mechanical reason for the work to be different?

I suspect that the reason that the simple models don’t accurately answer the basic question is the inability of a human to ‘benefit’ from negative work.

No, that is not the reason far any differences, because that inability exists in both cases.

What is different between treadmill and ground, are the visual cues (fixed vs moving surrounding) and the spatial limitations due to the size of the belt surface (no tolerance for variable walk speed). These can lead to a different gait pattern and muscle activation.

The forces are different in the 2 cases, not (necessarily) the gait.

What forces are different despite same gait pattern and why?

 

[jbriggs444]

I don't believe that a difference in observable gait is required. The forces are different in the 2 cases, not (necessarily) the gait.

Given identical gait, the forces are identical in the two cases.

 

[anorlunda]

I think the posters are ignoring the very clear way @russ_watters delineated the problem in #39.

Please note: the OP and the post quoted were about "exercise value", which is different than mechanical work. We've for the most part been assuming the motion is identical in the various cases, making the "exercise value" the same because the mechanical work done is the same.

The question is not mechanical work, force*distance. It is human biological work, which obey the mechanical laws of physics but it also much more. Standing still consumes work in the body. We could say that mechanical work establishes the floor of biological work, but the average and peak values of biological work (exercise) are necessarily higher.

If everyone continues debating while thinking of differing definitions of work, the debate is endless. So please, let's stick to the OP's question about "exercise value" or biological work.

 

[Dullard]

anorlunda:
I agree. That's really at the heart of what I'm arguing. The 'net' work for the 2 cases is the same, but the ''peak-to-peak' is larger for actual climbing. My example with the cart was an attempt to illustrate that there are real differences in the forces.

 

[A.T.]

The 'net' work for the 2 cases is the same, but the ''peak-to-peak' is larger for actual climbing.

Do you mean that there is more antagonist muscle co-contraction, which uses more energy, despite the same external work? This is theoretically possible, but why would it be more on ground?

 

[anorlunda]

This is PF. We can do still better in making this a quality debate.

V02 https://en.wikipedia.org/wiki/VO2_max is a qualitative metric of exercise used by doctors. Rather than personal opinions, let's see some peer reviewed studies citing V02 for running, stairmasters, and treadmills. Or any other objective measures. But please let's stop with personal opinions unsubstantiated by references.

I would prefer to see this thread become better quality than to close it.

 

[russ_watters]

I don't believe that a difference in observable gait is required. The forces are different in the 2 cases, not (necessarily) the gait.

This is quite simply false. The force in both cases is exactly your weight.

 

[russ_watters]

anorlunda:
I agree. That's really at the heart of what I'm arguing. The 'net' work for the 2 cases is the same, but the ''peak-to-peak' is larger for actual climbing. My example with the cart was an attempt to illustrate that there are real differences in the forces.

Except that the cart example doesn't actually match the exercises. The cart example you gave is what happens if you hold on to the handlebars. We all agree that if you do that, it reduces or eliminates the exercise value.

Please: apply some numbers: A person weighs 170lb and walks smoothly up the stairs or stairmaster. What is the force applied?

Any actual experiment comparing the amount of exertion required to walk on a treadmill/stairmaster with the effort required on their geometrically equivalent low-tech counterparts empirically demonstrates that they are not equivalent in terms of effort (it isn’t even very close). I’ve done it, and don’t know of anyone (who actually did an experiment) who disagrees.

That is shocking to me. If there wasn't a significant exercise value, there would be no point to the exercise! Maybe you are using it wrong; are you holding on to the handlebars? I've seen people at the gym leaning hard on the Stairmaster handlebars.

 

[russ_watters]

Climbing stairs is a great exercise to raise the heart rate and sculpt a strong, lean lower body... if you're doing it right.

"I see many people placing close to half of their body weight leaning on the rails that they give you as just protection so you won't fall," Mark Hendricks, Group Fitness Manager at Greenwich Avenue Equinox says. "It's a safety issue not to place your hands on the handrail. That being said, there should never be pressing/pushing down on them."

When you push down on the rails, it decreases the load on your legs and glutes. "The heavier you load your muscle, the more muscle fiber you activate and essentially the more change you make in your muscle,"

https://www.self.com/story/the-mistake-youre-making-at-the-gym-stairmaster

So are you using it wrong?

 

[Dullard]

The cart example just provides a simple way (the tension in the rope) to illustrate the forces. The wheels eliminate any 'gait' questions.

I never claimed that a treadmill/stepper was 'no exercise' - just not as much. I only did that after others claimed that the required effort was identical. An open-minded reading of post #40 should be sufficient to make my point about the 'difference in forces' to any who are likely to grasp it. I won't be posting in this thread any more.

 

[russ_watters]

The cart example just provides a simple way (the tension in the rope) to illustrate the forces. The wheels eliminate any 'gait' questions.

I never claimed that a treadmill/stepper was 'no exercise' - just not as much. I only did that after others claimed that the required effort was identical. An open-minded reading of post #40 should be sufficient to make my point about the 'difference in forces' to any who are likely to grasp it. I won't be posting in this thread any more.

Sorry, but it isn't. You are really just handwaving and saying irrelevant things (a person on a stairmaster is not supported by a rope hanging from the ceiling). If you do choose to return to the thread, I must insist you start using numbers: A person weighs 170 lbs. What force does he apply to the stairs/stairmaster in a smooth/steady state climb?

 

[Tom.G]

Here is a start on using numbers. (looks like they may just give more to argue about!)

The formatting was not maintained but this was found as Category 02 at:
https://sites.google.com/site/compendiumofphysicalactivities/references

It shows that walking up a down escalator at 70 steps per minute uses 7% more energy than a StairMaster at 77 steps per minute.

From pg 7 of 17: https://632e345c-a-62cb3a1a-s-sites.../02-ConditioningExercise-2011CompendiumPA.pdf

02065 Stair treadmill ergometer, general 9.0
Average of 5 measures below

(Device)              (Speed)               (Energy?)          (Reference)
 StairMaster® , 60 steps/minute, level 5      6.51         (Butts, Dodge et al. 1993)

 StairMaster® , 77 steps/minute, level 7      7.99         (Butts, Dodge et al. 1993)

 StairMaster® , 95 steps/minute, level 9      9.48         (Butts, Dodge et al. 1993)

 StairMaster® , 112 steps/minute, level 11   10.98         (Butts, Dodge et al. 1993)walking up a descending escalator,
,                70 steps/minute,              8.56        (Bassett, Vachon et al. 1997)

 

[russ_watters]

Here is a start on using numbers. (looks like they may just give more to argue about!)

The formatting was not maintained but this was found as Category 02 at:
https://sites.google.com/site/compendiumofphysicalactivities/references

It shows that walking up a down escalator at 70 steps per minute uses 7% more energy than a StairMaster at 77 steps per minute.

From pg 7 of 17: https://632e345c-a-62cb3a1a-s-sites.../02-ConditioningExercise-2011CompendiumPA.pdf

I've requested a copy of the full paper to check the methodology.

...And tonight at the gym I'll count how many people on the stairmaster are holding on to the handlebars...

 

[jbriggs444]

In a stairmaster, as distinct from an escalator, I believe[d and was incorrect] that the idle leg is not lifted completely by the user but gets a "free ride" up on the ascending pedal. This amounts to positive work being done by the ascending pedal on the user. Although external work done on the user cannot normally be recovered as available energy, in this case it serves to elevate the leg. That is a task that the user would otherwise need to call on his hip flexors to perform.

In addition to recovering the energy needed to lift the idle leg back into position for another power stroke, the force applied by the power leg on its downstroke is reduced by whatever fraction of the user's weight is on the rising pedal. In effect, the work recovered from the rising pedal is doubled -- the same figure appears twice in the energy budget.

Edit: Thank you, @russ_watters. I stand corrected.

 

[russ_watters]

In a stairmaster, as distinct from an escalator, I believe that the idle leg is not lifted completely by the user but gets a "free ride" up on the ascending pedal.

Please note: "Stairmaster" is a brand name, not a type of machine. I think the assumption here needs to be that we are talking about the type that uses actual steps, not the type that uses pedals:

Not:

 

[.Scott]

Stairmaster: the 'F' in 'FdotdS' is body weight (max). station-keeping.

Stairs: the F is body weight plus the force required to produce a net upward velocity. If the force were only body weight (or less), no 'climb' could occur. The add'l force is not trivial.

Let me take a shot at this.
I believe what @Dullard is saying is that as a person walks up stairs they effectively pause at each step. Then they need to reaccelerate to move to the next step.

The key is this: When they pause, they pause relative to the steps. And when they accelerate, they accelerate relative to the steps. If a person pauses on an escalator, they don't stop gaining altitude. And when they resume their climb, they only need to increase their vertical velocity by as much as they would if the steps were not moving.

Bottom line is: There are difference in the forces during the transitions from a stationary floor to moving step or vice versa. But once you are on the steps (and presuming you are not holding onto the bar), you will exert the same amount of energy per step whether the steps are in motion or not.

 

[russ_watters]

Let me take a shot at this.
I believe what @Dullard is saying is that as a person walks up stairs they effectively pause at each step. Then they need to reaccelerate to move to the next step.

Agreed, though there are two ways around this:
1. We've specified and he's accepted that the gaits for each will be the same.
2. To make the analysis easier, we've tried to specify uniform motion, but it isn't clear if he's accepted. Perhaps he (and you)think it matters, but it doesn't:

The key is this: When they pause, they pause relative to the steps. And when they accelerate, they accelerate relative to the steps. If a person pauses on an escalator, they don't stop gaining altitude.

*Losing* altitude. They are going up the down escalator.

And when they resume their climb, they only need to increase their vertical velocity by as much as they would if the steps were not moving.

Which is exactly the same velocity as would be on stationary steps. Otherwise they are just plain walking slower on the escalator.

...once you are on the steps (and presuming you are not holding onto the bar), you will exert the same amount of energy per step whether the steps are in motion or not.

Given what you said above, it surprises me you still agree the energy is the seame, but I'm glad you do! ...maybe it was just a typo?

 

[.Scott]

*Losing* altitude. They are going up the down escalator.

I was taking the more normal scenario of going up the up escalator. So whe the pedestrian pauses on the escalator, they are still going up. And when the resume, they are restarting from upward vertical velocity - not from stationary.

 

[PeroK]

I was taking the more normal scenario of going up the up escalator. So whe the pedestrian pauses on the escalator, they are still going up. And when the resume, they are restarting from upward vertical velocity - not from stationary.

That makes no difference. That's just a constant upwards velocity relative to the Earth. You know enough physics to see that you simply have two inertial reference frames there: the surface of the Earth and the moving escalator. Newton's laws apply identically in both.

 

[russ_watters]

I was taking the more normal scenario of going up the up escalator. So whe the pedestrian pauses on the escalator, they are still going up. And when the resume, they are restarting from upward vertical velocity - not from stationary.

Ok, but that scenario isn't on the table so I'm not sure why bring it up or what you are trying to say about it...but it doesn't feel right.

Specifically, stationary is stationary. What matters is if the person is stationary or moving with respect to the steps. Whether the steps are moving up, down, left or right with respect to Earth makes no difference.

 

[.Scott]

That makes no difference. That's just a constant upwards velocity relative to the Earth. You know enough physics to see that you simply have two inertial reference frames there: the surface of the Earth and the moving escalator. Newton's laws apply identically in both.

Yes. I understand that - and it was my point. I was addressing remarks by @Dullard. I was trying to describe this in the same terms that he was using.

Ok, but that scenario isn't on the table so I'm not sure why bring it up or what you are trying to say about it...but it doesn't feel right.

Specifically, stationary is stationary. What matters is if the person is stationary or moving with respect to the steps. Whether the steps are moving up, down, left or right with respect to Earth makes no difference.

I believe that if @Dullard understands what I posted, he would also understand the other scenarios.

 

[Tom Hammer]

Let us consider climbing an incline on Earth that is the same angle as the stair climber and is parallel to the Earth's motion through space around the sun. Obviously relative to the sun the incline is moving. Let us approximate that the velocity is constant. The hill climber does not notice the motion and we calculate his work done relative to the center of the earth. The athlete on the stairmaster is analogous. The confusion results from the motion being obvious in the case of the stairmaster.

 

[votingmachine]

However, use of any external aids that are not moving down (e.g. the hand holds) does make a difference. To get the full value you mustn't pull on anything that is not descending. The people you see on the treadmill holding the bars, or pushing down on the handholds on the stairmaster are significantly reducing the work done. That's similar to being pulled uphill by a ski-tow.

Hanging on the bars is a HUGE difference. I see people locking their arms and bearing a significant amount of weight, reducing the work compared to a the same number of steps on real stairs.

The treadmill discussion brought up two differences between the treadmill and a track that seemed important: elastic rebound from the rubber tread stretch, and elastic bounce from the treadmill suspension. If there is a rebound or a lift provided, that will reduce the work. I don't know the mechanism and there are many different "stair" machines. There are differences in stairs themselves, say between a bouncy bleacher, and a concrete stair. I assume people adapt their gait and timing to take advantage of natural rebounds.

I run stairs in a ski conditioning class every fall. I don't currently run stair machines, but years ago, when I tried them, they seemed clunky and a bit odd.

An even larger difference is that in my fall conditioning class, there is an instructor and other people running. I have never pushed with the same intensity as when I am in that group, with those instructors. There is some human psychological benefit to being in a group that is told to do something intense for the next two minutes. You just don't quit. Bottom line: we are all a bit lazy, and it does not surprise me that stair machines get used at less than the maximal work, which would probably be as good as real stairs.

Air resistance seems like it would be a negligible difference between stair machines and stairs. No one is THAT fast on stairs.

 

[russ_watters]

Hanging on the bars is a HUGE difference. I see people locking their arms and bearing a significant amount of weight, reducing the work compared to a the same number of steps on real stairs.

The treadmill discussion brought up two differences between the treadmill and a track that seemed important: elastic rebound from the rubber tread stretch, and elastic bounce from the treadmill suspension. If there is a rebound or a lift provided, that will reduce the work. I don't know the mechanism and there are many different "stair" machines. There are differences in stairs themselves, say between a bouncy bleacher, and a concrete stair. I assume people adapt their gait and timing to take advantage of natural rebounds.

I run stairs in a ski conditioning class every fall. I don't currently run stair machines, but years ago, when I tried them, they seemed clunky and a bit odd.

An even larger difference is that in my fall conditioning class, there is an instructor and other people running. I have never pushed with the same intensity as when I am in that group, with those instructors. There is some human psychological benefit to being in a group that is told to do something intense for the next two minutes. You just don't quit. Bottom line: we are all a bit lazy, and it does not surprise me that stair machines get used at less than the maximal work, which would probably be as good as real stairs.

Yes, if we want to get into the weeds (and maybe we do, for the sake of completeness), the "same gait" assumption isn't necessarily true and almost certainly explains the differences in actual energy use. To address (agree with) a couple of your examples:

I have a treadmill that claims shock absorption. I don't know if that helps (elastic) or hurts (inelastic), but clearly different surfaces (asphalt, grass, sand) have an impact on running energy consumption.

I don't use a stairmaster, but I have tried an elliptical machine a couple of times and I really hate it. My feet are spaced too far apart and I think the stride length isn't optimized for my height (I'm 5'7") and as a result, I feel myself leaning back and straining to stay upright on it. I would think this would not apply to the stair-stepper style, but the steps need to be the exact right depth and height to compare with real stairs.

And not for nothing, but I wear a heart rate monitor while I exercise and find that my heart rate on a real bike vastly exceeds that on a stationary bike. It will be something like 150 on a stationary for half an hour to an hour and 170 on a real bike, for 2-4 hours. I think most of this is explainable as my body's attempt to keep cool when biking outside when it is warmer, but I really can't be sure. I also tend to have too regular of a pace on a stationary, when variability is said to help.

Regarding classes, I've never done one so I'm not sure I should comment, but a buddy of mine told me once he couldn't believe how much he would sweat in a spinning class vs biking on his own. This confuses me; I feel that if you aren't destroying yourself you aren't working hard enough, and a person should be able to make that happen on their own. But he was never an athlete whereas I did a lot of athletics in high school (not to mention the Navy), so I've learned what it feels like to push myself. Perhaps he didn't know - until someone beat it out of him - that he could be working harder.

 

[A.T.]

I've requested a copy of the full paper to check the methodology.

Looks like the numbers are from different papers, by different authors, with different subjects and likely different step heights (if they even used the stair version of the stairmaster, not the pedal one).

 

[OldYat47]

... which is false. It doesn't matter whether you employ a funny walk, you cannot cheat gravity.

"Funny walks" aside, the definition of work is force X distance. So repeatedly moving one's center of gravity up and down is more work per the technical definition. Stepping to match the machine's speed so your center of mass remains at the same elevation is less work per the technical definition. Whether or not that's more exercise (say, burning more calories or putting more stress on muscles) is another question. For me it's more difficult physically to do the latter.

 

[jbriggs444]

"Funny walks" aside, the definition of work is force X distance. So repeatedly moving one's center of gravity up and down is more work per the technical definition

It is the dot product of vector force times vector distance. It can be negative. If you bounce up and down, you do zero net work (albeit expending much effort).

 

[russ_watters]

"Funny walks" aside, the definition of work is force X distance. So repeatedly moving one's center of gravity up and down is more work per the technical definition.

Obviously, if you have a different gait you may use more or less energy. The question can't even be addressed without the assumption of a common gait.