Stair machine Vs stairs. which is harder? I had a big argument at the pub about the stair machine being easier than actual stairs, and all the people there disagreed, saying that the only difference is air resistance? Are they kidding?
My point was that, as the stairs are moving in the same direction as you, you are exerting less force to maintain you torso's position; i.e. $mg = F_{\text{stair}} + F_{\text{leg}}$ (when climbing a stationary stair $F_{\text{leg}} = mg$)
The only time where this wouldn't be true is if the stair was stationary, you push yourself up, then after moving your body weight up, the stair moves down and becomes stationary again. But otherwise, the stair and your legs are moving in the same direction and the force (work?) required to work against gravity to push yourself up against the stair is less. Proof in the pudding is that, if the stairs move faster, the force exerted per stair is less
Is there a better way to explain this? It was infuriating. I think it has something to do with a work balance equation, but a figure would be better.
 A: Stair machines are not exactly equivalent to stairs for a few reasons, but not  due to the fact that you stay at the same height.
In real stairs, the impact of your foot with the stair will be quite jarring (you'll use extra muscles for stabilization).  The accelerations at the start and end of the step will tend to be different than the mechanics of an exercise machine.  The machines may have hand bars for stability.  You tend to use those in a much different way than you would a handrail in stairs.
But for the basic concept of the work your legs do, it can be similar.  In the staircase your leg is exerting force to move your body upward against gravity.  On the machine, your leg is exerting force to keep your body at the same height as the platform descends.
From a simplistic physics standpoint, this is very similar to walking to maintain your height on a down escalator.  It takes just as much power to hold your position when that device is going down at some speed as it does to walk up a staircase at the same speed.
Is the work done walking up an escalator in the same speed and opposite direction of the escalator zero?
From a biomechanical standpoint, the way the muscles engage with the steps and the gait you use may be wildly different, leading to differences in effort and utility.
A: If you do not use the handrails on the stairmaster, and neglect air resistance, the stairmaster is exactly the same as stairs. This is just basic Galilean relativity: there is no physical property that changes when you are still versus when you are moving at a constant velocity.
Note that if you stay in the reference frame where the stair climber is stationary, and compute the work done by the climber’s foot to the ground, you will find it is identical in both cases. The fact that some other unrelated forms of work in different reference frames are not equal doesn’t have any bearing on the problem.
A: Nobody said that doing the stair master is not doing any work; you're still doing work, but less. The faster the stair master moves, the less work you do (more cardio but less muscle work against gravity). To have the same effect or close to real stairs, the stair master would have to be very slow, in a way that you can push yourself up before the stairs go down. But the problem there is waiting for the next step, so it would missing the point.
