Work done running on an inclined treadmill

[A.T.]

If you want to argue with the researchers speculations...

What? I just wrote that an elastic board is obviously not equivalent to a non-elastic road.

Be sure to recognize that running outdoors, you run against air resistance.

Mentioned many times already.

Everything has already been said, but not yet by everyone. -Karl Valentin

 

[votingmachine]

You keep responding like you are trying to clear things up with a 5 year old. I am sure that is not your intention. Nor am I trying to pull a childish trick ... and if it appears I am, my apologies.

 

[Herman Trivilino]

If you ignore the energy losses due to heat transfer (from your body to the surroundings) and the moving of the arms and legs (since I'm assuming these to be about the same in climbing a hill as they are in running on an inclined treadmill) the chemical energy generated by your body's biological processes is equal to the gain in potential and kinetic energy of the center of mass of your body. Thus when you climb a hill you generate more chemical energy because you are raising the center of mass of your body, and increasing its kinetic energy.

A lot of the confusion in these types of discussions arises from a fundamental error made in introductory textbooks in the way work is introduced, an error that you see being corrected in many of the newer editions. The best way to start to understand this confusion is to look at the work done that's associated with a dissipative friction force. For example pulling a block at a steady speed across a level table top. The force you apply does, say, 100 J of work on the block. If you then say that the friction force does -100 J of work, the net work done is zero and the change in kinetic energy of the block is also zero. But how then do you account for the fact that the block and table top got warmer? The issue here is how to generalize the concept of work that's introduced in the study of dynamics to the concept of work that's introduced in the study of thermodynamics. The physics education literature has a vast discussion of this issue. The 100 J of work done by you produces an increase of 100 J in the internal energy of the block and the table, there is in the thermodynamic sense no work done by the friction force.

 

[jbriggs444]

Thus when you climb a hill you generate more chemical energy because you are raising the center of mass of your body, and increasing its kinetic energy.

This has been discussed to death in this thread already. When you run on a treadmill, the chemical energy (that is not wasted on biological or mechanical inefficiency) goes into work done on the treadmill. When you climb a hill, it goes into work done raising the center of mass of your body.

Six of one, half dozen of the other. To a first approximation, the same amount of chemical energy is used either way. [With apologies to those arguing about the second approximation]

 

[votingmachine]

That effect appears to be a figment of the imagination. It has no basis in physical reality. There is no magical "I can stop running and let gravity do part of the work" mechanism in action.

One other thing that occurs to me is that there has to be a speed micro-variation in the treadmill. The motor powering the treadmill has a response curve. The stride may be such that both legs are airborne, and no load is on the motor. The front foot strikes, and drives. Finally it lifts and both feet are airborne again, with the other foot the lead for the next stride. The load profile would be a crazy one. Combine that with the stretch of the treadmill rubber, and it could deliver a boost to different people who have different cadences, depending on how they synchronize with the load response. If there is a power return from elasticity, and from motor load response times, that would also make treadmills easier.

The motor is generally software controlled, with the target speed selected. I have no idea if the software tries to predict the jerks in the load that accompany running. It would make sense to have a flywheel. I've never thought about it much, but people jump onto the siderails, play with their phone, and then jump back onto the belt ... that has to be awful for motor life.

I'm not questioning the concept that the running motionless on the ideal treadmill simulates moving in the real world. Just pondering where the real treadmill is different.

 

[Grinkle]

I have no idea if the software tries to predict the jerks in the load that accompany running.

I don't think they do - they have closed loop velocity controllers that react to the varying load, but as far as I know they don't have any type of feed-forward to predict a variance.

Combine that with the stretch of the treadmill rubber,

Running surface definitely matters. My high school cross country coach credited the reduction of the 4 minute mile to a common place achievement to artificial track surfaces (as opposed to old school dirt tracks).

 

[A.T.]

Thus when you climb a hill you generate more chemical energy because you are raising the center of mass of your body, and increasing its kinetic energy.

This argument was debunked all over this thread. Did you read any of it?

Analyse an ideal inclined treadmill from the inertial frame, where the upper belt surface is at rest. Here you continuously move upwards and gain energy, just as you would on a real hill.

 

[votingmachine]

This argument was debunked all over this thread. Did you read any of it?

Analyse an ideal inclined treadmill from the inertial frame, where the upper belt surface is at rest. Here you continuously move upwards and gain energy, just as you would on a real hill.

I read that the same way as in post #124:

When you run on a treadmill, the chemical energy (that is not wasted on biological or mechanical inefficiency) goes into work done on the treadmill. When you climb a hill, it goes into work done raising the center of mass of your body.

Six of one, half dozen of the other. To a first approximation, the same amount of chemical energy is used either way. [With apologies to those arguing about the second approximation]

On the hill your chemical engine pushes thru the legs and lifts the body. On a treadmill, your chemical engine pushes against the band and puts a load on the treadmill system. I read that as calling attention to the work done thru the treadmill friction, when you look at it from the "rest" frame next to the treadmill.

Perhaps I misread, but I think it was the same argument made all thru the thread, but with a clarification about friction dissipating heat energy.

(since I'm assuming these to be about the same in climbing a hill as they are in running on an inclined treadmill)

 

[jbriggs444]

Thus when you climb a hill you generate more chemical energy because you are raising the center of mass of your body, and increasing its kinetic energy.

Perhaps I misread, but I think it was the same argument made all thru the thread, but with a clarification about friction dissipating heat energy.

I am not certain what argument you refer to. If it is the one above by @Mister T then I see no mention of friction.

 

[votingmachine]

I am not certain what argument you refer to. If it is the one above by @Mister T then I see no mention of friction.

Perhaps you are right. I might have misread. I just looked carefully, and there is a gap in the dots I connected. I read your post immediately after/simultaneously and put the friction he mentioned into your "work done on the treadmill" context.

... and I've just gone back and re-read again. Now I'm puzzled by the post. As I said, I checked the thread AFTER your response and read them back to back. I thought they were saying the same thing, with an aside about heat.

 

[Herman Trivilino]

This argument was debunked all over this thread. Did you read any of it?

Some of it.

In the second paragraph of Post #123, the work done by friction that I mention there is sometimes called pseudo-work, or whatever name you want to call it, to distinguish it from work that is thermodynamically valid (that is, able to be used in the 1st Law of Thermodynamics). I was thinking that the work done on the treadmill was of this type, but then I re-thought things when I saw what @jbriggs444 wrote in Post #124.

 

[fresh_42]

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