Stairmaster Physics: Exploring Exercise Value & Mechanics

[MasterTheStairs]

Apologies if this is a repeat of previous threads, I did search and can't see an answer to my question.

I'm a fitness trainer and a subject that comes up with clients from time to time is the physics of the stairmaster. Confusion reigns as some influential commentators have said that it has no exercise value "as the step is falling away". I'm satisfied that they just betray a very incomplete understanding of the physics, as the fact is that so long as the relative positions of the mass and point of application of the force are either forced apart (as in a squat), maintain their distance (as in any isometric exercise or the paused phase at the top and bottom of a squat just before lowering or return) or only allowed to come together at a controlled rate (as in the eccentric phase of a movement or the deliberate slowing of a movement like the squat mid-exercise, or where there is force being applied which is less than the mass, so that the force is overcome and the mass moves anyway) by virtue of the application of muscular force, then work is being done and exercise value is achieved. The fact that most of the mass of the body maintains its position is irrelevant. Besides my understanding of the physics, the fact that anyone using a stairmaster sweats, pants and gets tired is evidence that work is being done.

So;
Am I broadly correct in my understanding of the physics?
If not, what am I missing?
Is there any easier way to explain this to clients or a resource I could post them to?

TIA for any help, it'll all be appreciated.

 

[anorlunda]

Welcome to PF and thanks for trying to be considerate.

If you searched inclined treadmill, you would find these two threads. I presume that the physics of stairmaster and an inclined treadmill are the same.

https://www.physicsforums.com/threads/fitness-treadmill-incline.937725/
https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/

 

[PeroK]

Apologies if this is a repeat of previous threads, I did search and can't see an answer to my question.

I'm a fitness trainer and a subject that comes up with clients from time to time is the physics of the stairmaster. Confusion reigns as some influential commentators have said that it has no exercise value "as the step is falling away". I'm satisfied that they just betray a very incomplete understanding of the physics, as the fact is that so long as the relative positions of the mass and point of application of the force are either forced apart (as in a squat), maintain their distance (as in any isometric exercise or the paused phase at the top and bottom of a squat just before lowering or return) or only allowed to come together at a controlled rate (as in the eccentric phase of a movement or the deliberate slowing of a movement like the squat mid-exercise, or where there is force being applied which is less than the mass, so that the force is overcome and the mass moves anyway) by virtue of the application of muscular force, then work is being done and exercise value is achieved. The fact that most of the mass of the body maintains its position is irrelevant. Besides my understanding of the physics, the fact that anyone using a stairmaster sweats, pants and gets tired is evidence that work is being done.

So;
Am I broadly correct in my understanding of the physics?
If not, what am I missing?
Is there any easier way to explain this to clients or a resource I could post them to?

TIA for any help, it'll all be appreciated.

Yes, it's easy to get it wrong. I got very confused when I first analysed it. There's no doubt, however, that the work done is essentially the same whether the stairs are moving down, or you are moving up the stairs.

The key physics argument is to consider the (inertial) reference frame moving down with the stairs. I don't know if there is a better argument that is more accessible to lay-people.

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.

 

[russ_watters]

Am I broadly correct in my understanding of the physics?

Yes.

Is there any easier way to explain this to clients or a resource I could post them to?

Other than the links @anorlunda provided, the definition of work is the simplest way to explain it: work = force x distance. The fact that it is the treadmill/stairmaster that is "moving" and not the user doesn't matter as long as your foot applies the same force over the same distance.

Or if you really want to blow their minds, you can point out that "moving" is a relative thing. It is perfectly acceptable to declare the stairmaster/treadmill to be stationary and the person to be moving.

 

[Dullard]

At the risk of living up to my name:

I believe that for the case of a treadmill/stairmaster, the effort is not trivial, but also not as large as the requirement for the equivalent fixed apparatus. Consider a user's leg (since that's what we're really talking about):
In the case of a fixed stair, the leg starts bent at the knee, the weight is shifted to that leg, and the entire body is elevated as the leg straightens. The leg 'sees' the weight of the body plus the force required to accelerate the body mass to the gravitationally superior position.

In the case of a 'stairmaster,' the motion looks the same, but the force on the leg is (at most) the weight of the body, and probably slightly less.

In short: The 'F' in the 'FdotdS' is smaller on a stairmaster.

 

[PeroK]

At the risk of living up to my name:

I believe that for the case of a treadmill/stairmaster, the effort is not trivial, but also not as large as the requirement for the equivalent fixed apparatus. Consider a user's leg (since that's what we're really talking about):
In the case of a fixed stair, the leg starts bent at the knee, the weight is shifted to that leg, and the entire body is elevated as the leg straightens. The leg 'sees' the weight of the body plus the force required to accelerate the body mass to the gravitationally superior position.

In the case of a 'stairmaster,' the motion looks the same, but the force on the leg is (at most) the weight of the body, and probably slightly less.

In short: The 'F' in the 'FdotdS' is smaller on a stairmaster.

Although appealing, that argument depends on the motion through the gravitational field being relevant. If you had three sets of stairs: one moving up, one at rest relative to the Earth's surface; and one moving down, then you wouldn't be able to tell which one you were on.

The point is that regarding the gravitational field you cannot distinguish between these three cases.

 

[Dullard]

I'm not sure that I follow your reasoning. Were I on one of the 3 stairs in your thought experiment, I would certainly be able to distinguish between them, unless my body was also moving at the experimental velocity. I understand what you're saying, but don't believe that the stairmaster (or treadmill) is equivalent to any of your 3 cases. The fundamental question is: is more work required to lift a body some distance than to maintain elevation as the 'floor' falls away? I say 'yes' (timidly).

 

[PeroK]

I'm not sure that I follow your reasoning. Were I on one of the 3 stairs in your thought experiment, I would certainly be able to distinguish between them, unless my body was also moving at the experimental velocity. I understand what you're saying, but don't believe that the stairmaster (or treadmill) is equivalent to any of your 3 cases. The fundamental question is: is more work required to lift a body some distance than to maintain elevation as the 'floor' falls away? I say 'yes' (timidly).

Certainly there is the potential for the interaction between your work and the stairmaster engine to create a difference between the two cases. And that, I believe, gets complicated. But, as far as the raw movement through a gravitational field is concerned, you cannot distinguish the cases.

Imagine you were in an elevator moving down at constant speed. And the elevator had some internal steps. You could not tell that the elevator was moving down and you were climbing steps moving down in the gravitational field. That would feel exactly like climbing the same steps with the elevator at rest or moving upwards at constant speed.

The basic operation of the stairmaster is the same. If you do nothing, you move down with the stairs. And, to avoid moving down with the stairs you have to climb them in the same way as you have to climb a stationary flight of stairs.

 

[Dullard]

As I said, I understand what you're saying. I have no issue with your elevator. My problem is with your last paragraph. I don't agree that the fact that I'll 'move down with the stairs' if I 'do nothing' makes the stairmaster equivalent to the 'whole system in an elevator'. I don't believe that 'you have to climb them in the same way.' It still boils down to the magnitude of the force on a leg. If climbing stairs were a series of infinitely fast exertions, where you 'pop' to the next step, I'd agree that the stairmaster is equivalent to stairs. The actual motion is (more or less) continuous - that leads to the difference is the required force - station-keeping vs actual climbing. Maybe I'm just confused.

 

[OldYat47]

How much work is done depends on the user. If your body is kept at the same height (leg extending so your foot speed matches the speed of the stair moving down) there is less work done than if you "boost" yourself up with every step (center of mass moving up and down some). Your leg is still retracting and extending either way.

But all that may be misleading from an exercise point of view. For example, if you just squat down half way, say, and stay there then no work is being done (no movement), but your leg muscles will certainly be under tension and you will feel the strain shortly. You can get a great deal of exercise doing isometrics where nothing is moving so no work is being done.

 

[jbriggs444]

How much work is done depends on the user. If your body is kept at the same height (leg extending so your foot speed matches the speed of the stair moving down) there is less work done than if you "boost" yourself up with every step (center of mass moving up and down some). Your leg is still retracting and extending either way.

This is distracting from the point at hand and is contrary to the physics definition of work. Let us not complicate matters by having the fellow climbing the stairmaster perform different gyrations than the fellow climbing a flight of stairs.

 

[MasterTheStairs]

Yes.

Other than the links @anorlunda provided, the definition of work is the simplest way to explain it: work = force x distance. The fact that it is the treadmill/stairmaster that is "moving" and not the user doesn't matter as long as your foot applies the same force over the same distance.

Or if you really want to blow their minds, you can point out that "moving" is a relative thing. It is perfectly acceptable to declare the stairmaster/treadmill to be stationary and the person to be moving.

That's essentially the way I've always looked at it, but you put it more clearly than I normally ending up doing Perfect, thanks Russ.

Thanks very much for all the contributions, much appreciated and I have some new angles for explaining it to the doubters. It's surprisingly hard to find resources that explain basic principles like this as they apply to exercise, so I really appreciate you guys taking the time to answer.

 

[MasterTheStairs]

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.

Absolutely and this is a bugbear of mine in gyms. Usually it's more easily solved than the Stairmaster discussion, "Let go of that f$%&&^ing bar" normally sorts it out

 

[Dullard]

PeroK:
I'm still pondering. If I understand what you're saying:

I go to the mall and find the escalators. I walk up the 'down' escalator at a rate which just maintains my elevation.
I go to the 'up' escalator and climb it at the same step-pace as was established on the 'down' escalator. My elevation will increase 2x the rate of just 'riding' the escalator.
Your contention is that these will feel identical to the climber. Is that right?

 

[russ_watters]

PeroK:
I'm still pondering. If I understand what you're saying:

I go to the mall and find the escalators. I walk up the 'down' escalator at a rate which just maintains my elevation.
I go to the 'up' escalator and climb it at the same step-pace as was established on the 'down' escalator. My elevation will increase 2x the rate of just 'riding' the escalator.
Your contention is that these will feel identical to the climber. Is that right?

Nobody mentioned escalators. They aren't the same as stairs or stairmasters and the differences present themselves both with the mount/dismount and if you look at energy instead of power.

 

[Dullard]

Hmmmm. Ignore mount/dismount. I have no idea what you mean about energy and power - My simple understanding is that the former is the integral sum of the latter. How is a stairmaster different from walking up the down escalator? How is walking up the 'up' escalator not just like walking up stationary stairs?

 

[russ_watters]

How is a stairmaster different from walking up the down escalator? How is walking up the 'up' escalator not just like walking up stationary stairs?

Stairs have fixed lengths. Escalators have variable lengths depending on how they are used. Stairmasters have variable lengths depending on how they are used.

If you only care about power in the steady state, all are equal. But if you want to integrate over the length of the trip to find the energy expended, they can all be different.

 

[cjl]

PeroK:
I'm still pondering. If I understand what you're saying:

I go to the mall and find the escalators. I walk up the 'down' escalator at a rate which just maintains my elevation.
I go to the 'up' escalator and climb it at the same step-pace as was established on the 'down' escalator. My elevation will increase 2x the rate of just 'riding' the escalator.
Your contention is that these will feel identical to the climber. Is that right?

Yes, both of these cases will cause identical power output, energy expenditure, and perceived effort to the stair climber.

 

[Dullard]

The original post included a reasonably accurate (IMHO) description of stairmaster vs stairs. Namely, that the stairmaster provides exercise, but requires less effort than the 'equivalent' stairs. I felt no need to pipe up - I agree. Subsequent posts (Russ and PeroK) essentially claim that there is no difference between the stairmaster and the stairs. I do not agree with that for reasons previously stated. Post #17 is completely indecipherable (to me). The stairs in my house are Hickory.

 

[cjl]

It isn't less effort though. It's identical, assuming you aren't bracing yourself on the handlebars or anything like that

 

[Dullard]

Yes, both of these cases will cause identical

It isn't less effort though. It's identical, assuming you aren't bracing yourself on the handlebars or anything like that

I don't agree. See post#5. A lot of money could be made betting on this.

 

[cjl]

You don't agree that the escalator case is identical? It's a simple galilean transformation...

 

[PeroK]

PeroK:
I'm still pondering. If I understand what you're saying:

I go to the mall and find the escalators. I walk up the 'down' escalator at a rate which just maintains my elevation.
I go to the 'up' escalator and climb it at the same step-pace as was established on the 'down' escalator. My elevation will increase 2x the rate of just 'riding' the escalator.
Your contention is that these will feel identical to the climber. Is that right?

Yes. Especially the case of walking up an up escalator. The effort must depend on your speed relative to the escalator. The speed of the escalator is irrelevant. And, in fact, the same applies to the down escalator.

If you wish to proceed with your mistaken analysis, you will have to relate the effort to the speed of the escalator. If you are walking up a down escalator does it get easier and easier the faster the escalator is moving down? If the escalator is moving down at 10m/s and you are running up the escalator at 5 m/s, is that easy? You're actually moving down at 5m/s, so how much work are you doing?

The only physically consistent answer is that the velocity of the escalator relative to the ground is irrelevant and only your speed relative to the escalator matters.

 

[Dullard]

I never claimed that my speed 'relative to the ground' mattered. See post # 5. I say that the 'F' in 'FdotdS' is larger for the case where I'm actually elevating my posterior in the gravity field (as opposed to just maintaining position). Or: you could go to the mall. We're talking about climber effort. If your analysis technique isn't centered on climber effort, it may produce incorrect results.

 

[russ_watters]

Yes, both of these cases will cause identical power output, energy expenditure, and perceived effort to the stair climber.

Please be careful with that. The four scenarios are not fully defined. You are assuming the time and distance is the same in all cases, but that was not specified and of course the whole purpose of an escalator is to make them different.

 

[Dullard]

No. steady state.

 

[russ_watters]

The original post included a reasonably accurate (IMHO) description of stairmaster vs stairs. Namely, that the stairmaster provides exercise, but requires less effort than the 'equivalent' stairs. I felt no need to pipe up - I agree. Subsequent posts (Russ and PeroK) essentially claim that there is no difference between the stairmaster and the stairs.

You misread: The OP described why the power output is the same and everyone else agreed. There has been no dissension until/except you. So...

I do not agree with that for reasons previously stated.

[edit] Oh, post 5:

I believe that for the case of a treadmill/stairmaster, the effort is not trivial, but also not as large as the requirement for the equivalent fixed apparatus. Consider a user's leg (since that's what we're really talking about):
In the case of a fixed stair, the leg starts bent at the knee, the weight is shifted to that leg, and the entire body is elevated as the leg straightens. The leg 'sees' the weight of the body plus the force required to accelerate the body mass to the gravitationally superior position.

There is no acceleration. That's your error.

 

[cjl]

Please be careful with that. The four scenarios are not fully defined. You are assuming the time and distance is the same in all cases, but that was not specified and of course the whole purpose of an escalator is to make them different.

I think it's introducing unnecessary pedantry to introduce different times, and given that the rates are identical, the distance is also identical (for the same time) relative to the escalator. It is less confusing to just state that the scenarios are identical, and from the perspective of the stair climber, they are.

 

[Dullard]

I'm going to try 1 more time. This is about effort required of the climber.

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.

I don't know another way to explain it. If you disagree with me, don't bet your 401K on being right (you aren't) You might go to the mall, or talk to someone who has actually walked on a treadmill/stairmaster and compared.

 

[cjl]

There is no force required for a net upward velocity beyond simply the weight of the stairclimber. Constant velocity requires the same force as no velocity.

To put this another way: If you were simply standing on the escalator but there was a scale between you and the stair, do you believe it would show your weight as higher on an upward traveling escalator than a downward one?

 

[berkeman]

If you disagree with me, don't bet your 401K on being right

Thread closed temporarily for Moderation...

 

[berkeman]

I'm going to try 1 more time. This is about effort required of the climber.

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.

I don't know another way to explain it. If you disagree with me, don't bet your 401K on being right (you aren't) You might go to the mall, or talk to someone who has actually walked on a treadmill/stairmaster and compared.

@Dullard -- Please lose the attitude, and please try to learn from the very valuable PF resource.

Thread reopened for now. Please respond in a substantive way to the helpful responses you have been provided so far. Thank you.

 

[OldYat47]

Walking up the down escalator at a pace that leaves you in the same vertical location is identical to the mechanics of a stairmaster-type machine.
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. If a user boosts themselves up quickly at each step they will be doing more work because their center of mass will be moving up and down more (force X distance). Quickly extend the leg while the step is high, stand on step as it lowers until the next upper step is in place, quickly step and extend, etc. A user pacing at the same rate as the machine will do less work (center of mass in the same vertical location), but their legs are still moving so some work is being done. And for exercise "value", no motion is necessary at all (isometrics, yoga as examples).

 

[PeroK]

Walking up the down escalator at a pace that leaves you in the same vertical location is identical to the mechanics of a stairmaster-type machine.
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. If a user boosts themselves up quickly at each step they will be doing more work because their center of mass will be moving up and down more (force X distance). Quickly extend the leg while the step is high, stand on step as it lowers until the next upper step is in place, quickly step and extend, etc. A user pacing at the same rate as the machine will do less work (center of mass in the same vertical location), but their legs are still moving so some work is being done. And for exercise "value", no motion is necessary at all (isometrics, yoga as examples).

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

 

[jbriggs444]

If a user boosts themselves up quickly at each step they will be doing more work because their center of mass will be moving up and down more (force X distance).

This is not correct.