Stairmaster Physics: Exploring Exercise Value & Mechanics

[A.T.]

"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.

In the inertial rest frame of the support surface the center of mass is moving in the same way in both cases (assuming same same gait style), thus the work done is the same in both cases.

This has been explained ad nauseam in the other threads:
https://www.physicsforums.com/threads/fitness-treadmill-incline.937725/
https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825

 

[OldYat47]

Shouldn't the inertial reference frame be the ground? The work isn't relative to the steps since gravity comes from the Earth. The work is the relationship between the Earth and the center of mass. Try changing the speed of the step and how quickly the stepping leg is extended. And again, this does not necessarily reflect the amount of exercise being done.

 

[PeroK]

Shouldn't the inertial reference frame be the ground? The work isn't relative to the steps since gravity comes from the Earth. The work is the relationship between the Earth and the center of mass. Try changing the speed of the step and how quickly the stepping leg is extended. And again, this does not necessarily reflect the amount of exercise being done.

That's valid on a large scale. But on the scale of a stairmaster the gravitational field is constant. Again think about an elevator moving at constant speed. You can't tell the velocity by dropping an object inside the elevator.

 

[jbriggs444]

work is the relationship between the Earth and the center of mass

The work done by what on what? In the case of a stairmaster, the device is absorbing work energy from the user and dissipating that energy internally. In the case of a stairs, gravitational potential energy of the climber is increasing. Either way, the muscles in the person's body have done the same amount of work.

 

[A.T.]

Shouldn't the inertial reference frame be the ground?

The motion relative to the Earth as such is irrelevant (assuming a uniform gravitational field for this small region). Only the relative motions between the human and support surface matter.

 

[russ_watters]

Shouldn't the inertial reference frame be the ground? The work isn't relative to the steps since gravity comes from the Earth. The work is the relationship between the Earth and the center of mass. Try changing the speed of the step and how quickly the stepping leg is extended. And again, this does not necessarily reflect the amount of exercise being done.

The reference frame can be whatever you want, as long as you do the calculation right(and relevant to what you want to know). But since we're trying to find the energy expenditure of the person, the easiest frame to deal with is the frame in which they are moving relative to what they are pushing against.

 

[MasterTheStairs]

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.

I'm going off-topic in my own thread, but if you mean biking outside, he's probably sweating exactly the same amount per effort, or at least very close, but the passage of air on a bike would mean the sweat evaporates faster so you simply don't notice it. On a spin bike, no air movement, usually higher humidity, particularly in a group, would just mean the sweat isn't going anywhere. Even further off-topic, depending on what you're training for, high intensity all the time is not a good idea, it's becoming a discredited model as you need an aerobic base for long-term improvement, so a roughly 80/20 low/high intensity regime is far more use, depending on exactly what you're aiming for. On topic, you're right about the machine I was referring to, I should have said stepmill rather than Stairmaster, to distinguish it from the paddle-stepper type.

Folks, thank you all so much again for the replies, they really are appreciated, interesting and useful. I'm also delighted with myself for being able to understand so many of them