incline on treadmill ---> how much elevation gain?

coop wrote:

You would still be lifting your foot (and therefor your whole body mass) the same height. And, in walking, one foot must be on the ground at all times, so there is no change in the horizontal distance either.

Why do I have to lift my whole body mass when I lift my foot? When I lift my left foot my body mass is being supported by my right foot, which is going down.

I can walk "up" the down escalator without ever moving the location of my center of mass.

coop wrote:Dukerdog, go to the airport and try it out.

I don't need to. I already know the answer.

JimFiore wrote:

duker, I agree that it would be worth going to the airport to find out, but quantifying the results may be difficult (observer effect).

You won't need to quantify the results. If the suitcases are nice and heavy it will be very obvious.

Jim, I'm sure you have some mechanical engineering or physics professor friends there at your college. Why don't you approach them with the escalator problem and see what they have to say?

duker, funny, I was thinking of flying it by one of the physics dept. guys. At the very least, it would be good food for thought in one of their classes.

I hate to get into one of these treadmill debates again, but I believe that some studies have found that, as incline increases, there is a greater discrepancy in energy expenditure between on-ground running and treadmill running than would be explained by differences in air resistance. In other words, elevation is gained more easily on the treadmill. In these matters, I would rely on lab results rather than analysis by experts in Newtonian mechanics.

You have to lift your whole body mass, maybe not all at once, but cummulatively in order to climb stairs.

You would be lifting your whole body mass to eventually be on the next step. I'm not ignorant enought to think that lifting your foot off the ground is equal to the whole body mass, but by the end of the process, you're whole body has been lifted the height of the steps in relation to the steps (not the ground!)

Your body is going down, but so are the steps of the escalator.

I don't see what the location of your center of mass in relation to the ground has to do with this. It should the location of your mass in relation to the previous step, which would be indentical for stairs or escalators.

If you can explain that to me, I'd appreciate it.

coop wrote:

You have to lift your whole body mass, maybe not all at once, but cummulatively in order to climb stairs.

Yes. If you are actually climbing stairs. But not on the escalator.

coop wrote:

I'm not ignorant enought to think that lifting your foot off the ground is equal to the whole body mass, but by the end of the process, you're whole body has been lifted the height of the steps in relation to the steps (not the ground!)

Moving your body relative to the moving steps does not change your body's potential energy. Moving relative to ground does.

In order to do work on your center of mass you have to move your center of mass against a force, in this case gravity. If all you do is hold your center of mass in the same place you do no work on your center of mass, even if there are steps, and other people, and airplanes whizzing past you as you do it.

That's not to say that you aren't doing work as you climb "up" the escalator. You have to move your legs back and forth, and up and down, and all of that requires you to do work on your leg mass. But you do that same work on your leg mass when you actually climb stairs, plus you do the additional work of moving your center of mass to raise it to the top of the set of stairs.

oldguy wrote:

I hate to get into one of these treadmill debates again, but I believe that some studies have found that, as incline increases, there is a greater discrepancy in energy expenditure between on-ground running and treadmill running than would be explained by differences in air resistance. In other words, elevation is gained more easily on the treadmill. In these matters, I would rely on lab results rather than analysis by experts in Newtonian mechanics.

Well if you are right about the studies, then both the lab and Newtonian mechanics are telling you the same thing, so you don't have to choose.

I think Dukerdog has done a good job of explaining this. I guess the confusion arises because people are used to the argument that running on a treadmill is equivalent to running on flat ground. So therefore running on an inclined treadmill must be equivalent to running up a hill. Dead wrong.

Inclining the treadmill changes the nature of the workout so your legs will work in different ways but it is not an accurate simulation of running up a real hill because you are not doing any work against gravity.

science guy wrote:

I think Dukerdog has done a good job of explaining this. I guess the confusion arises because people are used to the argument that running on a treadmill is equivalent to running on flat ground. So therefore running on an inclined treadmill must be equivalent to running up a hill. Dead wrong.

Inclining the treadmill changes the nature of the workout so your legs will work in different ways but it is not an accurate simulation of running up a real hill because you are not doing any work against gravity.

Where did the gravity go?

26.2 sucks wrote:

I purchased a great training log at

http://www.intensesport.com

that has a treadmill conversion chart. It tells what various speeds and inclines on the treadmill are equivelant to running outside.

You wasted your money. Why is it so important that your treadmill workout is EXACTLY like your outdoor workout when every single workout you do outside is DIFFERENT?

duker, I asked one of my physics prof buddies. He says barring changes in biomechanics and similar effects, the two are equivalent. To simplify things (to avoid angles) he just used a motorized ladder. His analysis concurred with mine. The motor does work against you equivalent to the PE you would've gained in the stationary scenario, hence your ending PE is 0.

JimFiore wrote:

duker, I asked one of my physics prof buddies. He says barring changes in biomechanics and similar effects, the two are equivalent. To simplify things (to avoid angles) he just used a motorized ladder. His analysis concurred with mine. The motor does work against you equivalent to the PE you would've gained in the stationary scenario, hence your ending PE is 0.

What you are saying is that I am doing work on (or against) the stairs. I guess I can believe that. It makes sense that the escalator's job is easier when I am on it than when I am not. If I am not walking "up" the stairs, then its job is made easier by the amount of potential energy I lose. If I am walking "up" the stairs, the escalator's job is no harder than if I am just standing there, so it must be getting energy from somewhere. That somewhere must be me doing work against it.

Of course I'm still going to try this out next time I'm at the airport.

You do work relative to the ground when you run up a hill (your center of mass undergoes a displacement relative to the ground as you move).

But on a treadmill, what's the equivalent reference point? THE BELT IS TO THE TREADMILL WHAT THE GROUND IS TO NORMAL RUNNING. That's what you guys were missing. Work is done in reference to the BELT as the belt moves under you, but you don't move in reference to the machine as a whole. Displacement relative to the machine as a whole is not what you're measuring. You measure displacement relative to what you're running on. The belt.

Of course, the belt loops under again - but you can treat the belt as a uniform, flat, continuing surface, since the curving part of the belt at any instant in time doesn't come into this anyway.

So you don't move relative to the machine. But relative to a belt moving downwards and back continually, you do undergo a displacement. Upwards relative to it, since you're stationary relative to everything else, and it is going down. Therefore you apply a force through a distance - work. Of course, it's not work relative to SOME reference points - but you do expend energy. You can feel that. And running is all about the energy expenditure.

Why are runners such dorks? Who cares how fast you are running your easy runs? Just run at a certain effort. I don't think the world will end if you run 7:10 miles while actually doing a 7:20 outdoor effort instead of your normal 7:15 miles. Just run what feels right. There is no true conversion b/c different muscles are used for inclines than wind resistance and levels of hydration can vary and affect pace indoors vs. outdoors. Just run how you feel please and stop telling people that you ran 9 miles at 6:47 pace. How silly!!!

Consider the following with the escalator example. Turn the escalator off. Run to the top (say, 100 steps). You have done work equivalent to Force*Height of escalator (ignoring horizontal movement). That's your PE. Trial two: Same as trial one but when you get to the top, turn on the escalator. In a moment you will be back at the bottom and your net PE=0. You do no work going down (you just stand there). The escalator motor does work to bring you down equal to -Force*Height, thus canceling your PE to produce a net of zero. Trial three: Just make the escalator move while you are on it for an equivalent number of steps (100 in this case). Your PE is still zero as you appear to not move to a stationary observer but you do the work of traversing 100 steps. Interesting point: to an observer who is riding down the escalator while you're running up, you appear to be climbing 100 steps, and thus gain the PE found in trial one, relative to the moving observer.

There are two key scientific papers to read if you want to really understand this. Both papers need to be found in print in a library since they are pre-internet.

The first paper does a nice job from first principles of physics and shows treadmill = overground. But, the empirical thinkers out there won't be convinced.

1. Van Ingen Schenau, G. J. Some fundamental aspects of the biomechanics of overground versus treadmill locomotion. Med. Sci. Sports Exerc. 12: 257–261, 1980.

The second paper compared real people running on a real treadmill and on a real road and measured oxygen consumption. The scientists sat on the hood of the car that went along side the runners outside. They compare level and uphill running. They found no differences when the slope of the treadmill was = to the slope of the road. This paper should convince the empirical thinkers.

2. Bassett, D. R., M. D. Giese, F. J. Nagle, A. Ward, D. M. Raab, and B. Balke. Aerobic requirements of overground versus treadmill running. Med. Sci. Sports Exerc. 17: 477–481, 1985.

Jack Daniels did a similar experiment at faster speeds and I think did find a small difference in oxygen consumption attributed to air resistance.

Here's to Rodger- you are the man. Finally someone gives real, scientific evidence, done by real scientists, to support the correct school of thought here. There is no more room for argument, no more thinking up crazy scenarios involving escalators or quicksand or motorized ladders. The first paper is key, and shows what people should have realized all along- physics tells you that there is no difference.

Interesting. My empirical skills would lead me to a conclusion which is in agreement with the first of the two papers mentioned. Leaving out wind resistance, the two running modes would be equivalent. But I have some difficulty with the second.

Still, even an experimental scientist has to be an empirical thinker up to a point, surely? Could you, using your empirical skills, come up with a justification in terms of the laws of physics for the findings of Basset et al, regarding the equivalence of the incline on the treadmill to the slope of a real hill? My own empirical skills keep telling me that working your legs and arms such as to stay at the same height relative to the ground would be a good deal easier than working them such as to raise your body through a hundred feet. Dukerdog's escalator analogy is one I can't find fault with.

PatB

In the study you refer to we ran all tests on the TM at 6:00 and 5:00 paces and on flat 1-mile long road at the same two paces, but in both north and south directions. We measured wind velocity during every run so we knew what the runner was facing (if running at 12 mph and the wind on the car was measured as being 20 MPH then we assumed the actual wind was 8MP, which always agreed with a wind guage not with the car). Ran mile, measured VO2, HR, blood lactate associated with each run. Rested 5 minutes between runs and went the other direction at the same speed and got the VO2, HR, lactate. First 2 runs at 6:00 pace then 2 more at 5:00 pace. All subjects returned to the same road on two other occasions so each ran 12 runs and since the wind varied over those different days we were able to have winds (both head and assisting in nature) of a variety of velocites (actually ranged from almost 0 to just over 16MPH). The only conditions under which the TM results equalled the overground results were when the tailwind was equal to the speed at which the runner was running -- no relative wind. Same results at both speeds we used. No grade involved

PatB wrote:

Dukerdog's escalator analogy is one I can't find fault with.

PatB, if you consider my escalator analogy from the perspective of the escalator rather than the person climbing, it becomes obvious that "climbing" the escalator must be as difficult as actually climbing stairs. The escalator can't tell whether I am simply riding it down or "climbing" to stay in the same place. In either case it has to work just as hard. So when I "climb" I must be doing work on the escalator equivalent to the potential energy I lose if I just stand there.

My intuition tells me it would be easier to "climb" the escalator than to actually climb stairs, but that only proves that my intuition, like everyone else's, can sometimes be misleading.

duder wrote:

Here's to Rodger- you are the man. Finally someone gives real, scientific evidence, done by real scientists, to support the correct school of thought here. There is no more room for argument, no more thinking up crazy scenarios involving escalators or quicksand or motorized ladders. The first paper is key, and shows what people should have realized all along- physics tells you that there is no difference.

"Real" scientists come up with crazy scenarios all the time in order to better explain, and better understand, concepts, i.e., Einstein's famous thought experiments. That's because "real" scientists consider it just as important, if not more so, to understand the truth than to simply know it.

Thanks for joining into the discussion after everyone has agreed on the correct answer though. Your after-the-fact commentary is appreciated.

Dukerdog, I think you've conceded too easily.

Let's shrink the problem down to one step. Is it easier to straighten your leg while the escalator sinks beneath you, and keep your centre of gravity in a constant position, than it is to straighten your leg on a fixed elevator and raise your body through one full step? The answer must be yes. It's a lot easier. And the reason is that in the first case you have to apply a force equal to your weight, while in the second it has to be greater than your weight.

Of course, in real life, the c.g position wouldn't be constant. We'd see your head bobbing up and down. And if the movement was as much as one full step in vertical distance, we'd say QED: you might as well be walking up a fixed escalator, because the work done is the same. But the movement wouldn't be anything like one full step, would it?

There is some faulty logic involved in looking at the "unawareness" by the escalator of the difference between riding the stairs down, and pedalling to stay in the same place. I have to point out that when you're riding down, you're helping the escalator. It's working less hard than it would if you weren't there.

If experimental science clashes with deductive or intuitive thinking, the fault usually lies with the latter. But not always. I'd like to know how long that slope was in the Basset experiment. I'd also like to know how they managed to allow for wind-resistance when finding an equivalence between the two conditions.

PatB