Physics Question - Hills on Treadmill

Mr Mountain wrote:

In other words, forget all the physics crap and just train at incline and you will see the benefits very quickly.

Certainly good training advice. But in general, no I won't forget all the physics crap, it's valuable stuff.

Borrowing from Mr. Einstein here...

Imagine that you are on an incline and surrounded on five sides by a box (open at the bottom). Now imagine that the box is moving at 8 mph in a straight line uphill. You will naturally run uphill at 8 mph to avoid the box smashing into you.

Look down at the surface that you are running on. It is traveling at 8 mph backwards relative to the box (and to you, since you are keeping up with the box).

Now, after running some time quite blindly, able only to see the (apparently) unmoving box (since you are keeping up with it) and the ground beneath you receding at 8 mph a strangely familiar voice comes through the sides of the box;

"Joe"

"Huh?"

"Joe, I've got some news for you"

"What?"

"You know that box that is moving at 8 mph with you?"

"Yeah, what about it?"

"Actually, it's not moving at all. It is perfectly stationary."

"What are you talking about? I'm running at 8 mph just to keep up with the thing."

"No Joe"

"No what?"

"No, you are not running to keep up with the box. You are running to keep up with the giant treadmill that you are on that is going at 8 mph. The box isn't moving at all."

"No way! I can tell that I am running up a real hill because...because...well because...I don't know, I can just tell"

"Joe?"

"What?"

"You shouldn't have skipped my physics class, Joe."

"Mr. Edelstein? Sh!t !"

What the heck wrote:

"No, you are not running to keep up with the box. You are running to keep up with the giant treadmill that you are on that is going at 8 mph. The box isn't moving at all."

Half an hour I would have snapped back...

"Yes, I thought it seemed easy. My heart rate's only 150 and I'm sure it's 160+ on this grade in the real world..."

But having thought about it a bit more, I think I was probably wrong. In both cases the extra power required (beyond what's needed for horizontal motion) comes out to

velocity relative to belt * sin(angle) * mass * gravity

Eating more humble pie, constant vertical movement is not the same as an accelerated frame of reference.

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Hills still rule.

Lets simplify this, say you have a rope that is being let down at a constant rate from the ceiling.

Do you expend less energy to "climb" and remain at the same height above the floor when 10 feet of rope is let out than to climb 10 feet of stationary rope?

Newton wrote:

Lets simplify this, say you have a rope that is being let down at a constant rate from the ceiling.

Do you expend less energy to "climb" and remain at the same height above the floor when 10 feet of rope is let out than to climb 10 feet of stationary rope?

I already conceded and switched sides 10 minutes ago. But that's a very good analogy, better than alpine cog railways and 10-mile-long treadmills.

pjb wrote:

This motor torque (as well as friction) is what is standing in for gravitational work on the treadmill. By the physics definition of work, you are not doing work against gravity because you are maintaining an equipotential spot in the earth's gravitational field. However, due to the reaction forces provided by the treadmill motor and friction, your free-body diagram is exactly the same, so you have to go through the same motions and do the same amount of work.

Now THIS is the answer I was waiting for. I knew that the work was performed somewhere, but simply didn't know where. I just knew that the two situations (uphill treadmill running and outdoor hill running)l HAD to be equivalent.

I also like the running in a box and rope analogies. Different ways of conveying the same frame of reference idea.

Sorry,

That wasn't meant specifically for you...that was just to try to clarify for everyone.

Also, thanks for the insight and humility another physicist. Your ideas pushed this thread to look deeper.

I'm not exactly sure what the previous poster meant by "friction" but I think it's something similar to what I have been thinking since page 1.

If you think about efficiency, your performance is going to depend highly on the amount of O2 your body requires to perform a specific task. With treadmill running versus running on solid ground, you are able to run at a higher efficiency than you normally would be. But I truly feel this only carries over up until a certain pace/effort. I think most runners would say they aren't able to hold a repetition pace for very long on the treadmill -- it's too awkward at that effort. However, I know that at an easy aerobic pace, a trained runner is going to have a lower V02 than they would outside. Yes, this is mainly due to wind resistance and grade. But the one thing I have yet to hear (unless this is what the previous poster meant) is the factor of friction, specifically static versus kinetic friction.

Now, when you are running on the ground vs the treadmill, the coefficient for static friction is higher than it would be if you were running on a treadmill (where the belt is running backwards as you push off, which creates more kinetic friction. There is always friction there - it's not as if work is not being done, but you are not doing as much work. I don't claim to know the math involved in this and would not be able to break it down in terms of joules or kcals or anything... but I feel this makes sense?

We beat this question to death back in December:

http://www.letsrun.com/forum/flat_read.php?thread=3833437

Short answer: From simply a work/energy point of view, yes, it's the same as running up a hill. There may be other differences, but they're not basic physics related.

I'm almost willing to admit I'm wrong :)

But Neliah gave me hope... I'll be sure to check out the other treadmill physics thread too (that I somehow missed in my boards search)

Even if it is the same from a work/energy point of view, I have major biomechanical concerns, but that's a different story altogether.

Think of it this way, when your foot is in contact with the treadmill your foot is not moving with respect to surface your foot is in contact with. Therefore the kinetic friction is not any higher than it would be running on solid ground.

Other than the difference in the coefficient of static friction between pavement and the belt on the treadmill, there is no appreciable difference in friction.

You are confusing the the term "coefficient of friction" and "friction", they are not the same thing.

What the heck wrote:

And to all those folks who think that treadmill running is magically different than "real" running, please go back to physics class. The only differences are the lack of wind resistance and the cushioning of the treadmill. The fact that you are not going anywhere and that you have no gain in elevation is completely irrelevant.

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Oh no, please don't say you want to start this nonsense again.

"With treadmill running versus running on solid ground, you are able to run at a higher efficiency than you normally would be."

No.

"Now, when you are running on the ground vs the treadmill, the coefficient for static friction is higher than it would be if you were running on a treadmill (where the belt is running backwards as you push off, which creates more kinetic friction."

Please say you are joking.

"but I feel this makes sense"

Hey, I really want to take this opportunity to acknowledge the validity, and truly the importance, of your feelings.

BUT THIS IS NOT ABOUT FEELINGS. THIS IS A PHYSICS QUESTION.

Please go back to the above quote by "What the Heck".

And please stop posting if you lack even the most basic understanding of simple Newtonian physics.

I think you assumption that you are not moving up is wrong. Every push off moves you up and you go back down to the same location after you land and the treadmill moves you down until the next push off.

I guess I'm convinced that the amount of work done, globally, is uniform between a graded treadmill and the road hill. I think that the biomechanics side of it is what is confusing to me... The fact that different muscles may be doing different amounts of work in the two scenarios. I found a fairly useful article (that reviews some other studies/papers) that addresses some of these points, including what I meant by the treadmill "pulling" your foot backwards to some extent.

Here's the link (yes, on facebook) and some highlights:

http://www.facebook.com/topic.php?uid=266027758213&topic=16822

HSR = hard surface running

TMR = treadmill running

Spatial Parameters:

A study by Riley et al., (2008) comparing HSR and TMR at the same speed (approximately 13.8 km/h) found that stride frequency was significantly higher and stride length shorter on a treadmill when compared to HSR. These results confirmed those of Schache et al., (2001) and Frishburg (1983) who likewise found increases in stride frequency and decreases in stride length when TMR.

Furthermore, both of these latter studies found a decreased swing phase and an increased stance phase when TMR versus HSR (Frishberg, 1983; Schache et al., 2001) indicating an increased period where the foot is in contact with the treadmill belt.

Biomechanical - Muscular Interactions and Differences:

As the tread belt rolls backward it drags the foot backwards, eliminating the need for the Gluteals and Hamstrings to pull the upper body forward thus making the movement easier; hence its potential lower energy cost (Frishberg, 1983). The Hip Flexors however, now have to work harder to bring the limb, which is being dragged backward, forward. Furthermore, the Frishburg (1983) study found that the lower limb was required to move through a greater range of motion in the stance phase when TMR (X=60.6 vs 54.5 deg). Similarly, Schache et al., (2001) found TMR to have a lower angle of hip flexion at initial contact and considered the increased hip extension position to be caused by the treadmill belt dragging the foot rear-ward. With this in mind, if the Hip Flexor muscles are tight, the increased hip range of motion requirement on a treadmill may cause the pelvis to rotate or the lumbar spine to hyperextend to release the tension on the hip as the limb is dragged backwards. This increased pelvic rotation and/or lumbar hyperextension, which typically occurs with fatigue (which increases stance phase duration) and at high speeds, places strain on the hips and lowerback and has the potential to cause a number of injuries.

It should be noted however that a study by Riley et al., (2008) found no significant differences in hip flexion/extension ranges or pelvic rotation between HSR and TMR. The subjects in this study (n=20) who were regular runners and ran at least 15 mi (24 km) per week, were, however, only assessed over a short period (no more than 15 consecutive gait cycles). Hence these runners would not have been subject to the impact of fatigue.

With the belt moving backwards, the ability of the gastroc-soleus complex (calf muscles) to push off is reduced (Riley et al., 2008; Baur, Hirschm, ller, M¸ller, Gollhofer, & Mayer, 2007) and these muscles must work harder in order to achieve an effective push off. This is one of the reasons why you tend to power walk when you transition from the treadmill back onto hard surface – your calf muscles have been activated more than usual for hard surface locomotion. Furthermore, research has shown that running on the flatter, predictable surface of a treadmill requires less ankle stabilization than that required for running across land, with muscles like the peroneals found to be less active when TMR (Baur et al., 2007).

So does this mean thread over? We have exceeded the bounds of the original question...bio-mechanics was never the issue.If anything based on what you have posted, treadmill running on an incline makes you less efficient i.e. it is harder than on an actual hill.

UHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH, no. Both of these posts below are posts of clowns.

Vegan Physicist wrote:

What the heck wrote:

And to all those folks who think that treadmill running is magically different than "real" running, please go back to physics class. The only differences are the lack of wind resistance and the cushioning of the treadmill. The fact that you are not going anywhere and that you have no gain in elevation is completely irrelevant.

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Newton wrote:

So does this mean thread over? We have exceeded the bounds of the original question...bio-mechanics was never the issue.

If anything based on what you have posted, treadmill running on an incline makes you less efficient i.e. it is harder than on an actual hill.

Well, I don't think I'm really exceeding the bounds. It does seem like global work completed must be uniform. But the biomechanical differences seem like they could affect how much work certain muscles are doing, which I think relates substantially to my original question: are you getting the same benefit on a graded treadmill v. a hill.

It seems like that answer is probably no, they're not the same benefit, though perhaps the differences aren't significant?

And yes, the biomechanical differences I pointed out may well mean that treadmill hill running is harder. Saw this on the other treadmill physics thread:

"We've found it actually costs you MORE (about 5-8%) to run up a hill on a treadmill compared to the same grade over ground. This doesn't relate to the added energy for cooling required on a treadmill since the trials were relatively short (<8 minutes), so a huge thermogregulatory effect wasn't a factor.

What we think, and I'm waiting for some foot pressure and force application measurements to prove it, is this...as was addressed by a previous poster. When running, the metabolic cost is primarily dictated by the rate of force application to the ground. This is why the faster you go, the faster you have to apply force to the ground and this requires recruitment of a greater volume of muscle. These newly recruited muscles require energy, and so your metabolic cost increases with speed.

On a treadmill running uphill (5-10% grade), the magnitude and direction of force application is "blunted" by the treadmill belt moving underneath you and "pulling" the foot back under your centre of gravity. In hill running, where the foot strikes slightly more in front of the centre of gravity compared to level running, less force is applied directly to the belt to re-elevate your centre of mass because the belt is moving under it. In overground running uphill, the foot contacts the ground and rather than being "pulled" under the centre of mass, the leg stays under the CoM for a slightly longer period of time. The leg relative to the ground (or belt) is moving slower in overground running compared to treadmill running, allowing a greater time for force application. This allows less total muscle to be recruited, and the metabolic cost is slightly lower.

jT"