Treadmill Physics Questions (Similar to Airplane Question)

Uncle Rico, You are not seeing this clearly. Of course I agree that there is movement relative to the belt that is moving backwards. But the basic OP question was whether momentum which is a factor in road running is also a factor when running on the treadmill. You would argue that if you are running the same speed on the road as the treadmill the momentum would be the same.I think my example of the block sliding onthe treadmill shows that to the runner (or the block) the momentum is not the same. When the treadmill stops the runner nor the block keep going forward. (Maybe from the perspective of some one stationary on the treadmill they might momentum but that doesn\'t help the runner)

Uncle Rico wrote:

psychic wrote:

Back to High School Physics with you

momentum=Mass*Velocity. On a treadmill, V=0

Back to HS physics? I\'ve already had my share, and I must have been decent at it or I would not have gotten my engineering degree. Velocity relative to the earth is zero yes, BUT velocity relative to the belt is not and that is all that matters. You have momentum relative to the belt. There are plenty of posts explaining why. If I had an infinitely long treadmill and you were standing on it blindfold while it was running you would not know that you were moving relative to the earth. Much like we don\'t see that the earth is rotating at 1000mph.

Ok, I'm not sure of the physics, but it seems like you are thinking along the same lines as me.

Here's a road running equivalent to your block experiment. A runner dragging a block is running counter to the rotation of the earth at exactly the speed of rotation. To an observer on the sun the earth appears to be rotating while the runner and block are staying perfectly still. At the same time the runner's Garmin has him clipping along at a shade over 1000 mph. Suddenly the rotation of the earth stops. To the runner it appears that the ground has suddenly accelerated to his speed and with no change in momentum, that is without feeling acceleration, he can stop running. His block stays at the end of the rope since there was zero relative velocity between it and the runner both before and after the world stopped. The observer on the sun still sees the runner and block as stationary. Any observer stationary in earth's reference frame is wondering why they've suddenly been catapulted to 1000 mph.

ventolin^3 wrote:

ask me nicely & i'll tell you what you need to run on a treadmill to =

3'26 or 7'20 or 12'37 or 26'17

Can you also impress us by telling us how many great treadmill races you have watched on TV? I know I personally have watched many great treadmill races on TV and thus consider myself an expert in the subject.

Conundrum -YOU are the one not seeing this clearly. See Citizen Runner's explanation. We have said it 100 different ways. You agree that the runner has momentum relative to the belt, but don't think that this has the same effect as in road running? Again, see citizen runner's post.

Ok yeah citizen runner, I think that example demonstrates your point pretty well.

sineCosine wrote:

So running downhill on land, my momentum naturally builds and I begin rolling along faster and faster. At first I had trouble visualizing this on a negative incline treadmill, but I suppose the equivalent of beginning to build momentum on the downhill treadmill is the end result of running off the front of it (given the speed is constant).

The difference is that treadmills are not a replacement for doing hills. When you run downhill, you are actually lowering your gravitational potential energy, hence it feels easy to pick up momentum. You don't get that effect on a treadmill (no change in elevation). Opposite is also true for running uphill. It costs you energy to raise your body up some physical elevation, something the treadmill can't do. That's not to say that it doesn't cost you more energy to run with the treadmill at an incline, it just shouldn't be equated with running the same incline hill.

All this goes out the window if you are holding on to the rail of the treadmill, which I have seen people do.

In practice here's a few practical reasons why treadmill running feels different than road running.

1) Calibration - if the treadmill speed is not accurate, it will feel like you're running harder or easier than you'd expect because you are in fact going faster or slower than you think. It's also possible that the treadmill surface has an incline so you are effectively running up or downhill more than you realize.

2) Wobbly running surface - if the treadmill deck is unstable under you it's like running across a rope bridge to some degree. I've seen claims which seem plausible enough that people tend to have longer ground contact time when running on treadmills and other wobbly surfaces. This would effectively ripple throughout one's running form affecting economy and stressing the body differently. It's also harder to relax and run well on treadmills with narrow belts and shorter decks. If the belt slips or there is not enough inertia in the belt/roller system the belt speed will slow with each footstrike due to friction between the belt and the deck behind it.

3) Stagnant air - on a treadmill the runner is stationary relative to the air so evaporative cooling doesn't work as well and he has a tendency to overheat. Aiming a fan at the runner helps a great deal.

Doing intervals and other varied speed workouts, one's acceleration is forced to match that of the belt which may not feel natural. This makes treadmill pretty limiting for sprint workouts.

Conundrum wrote:

If the belt suddenly stopped, a block being slid on the treadmill would NOT move forward. It has no momentum. Try it. Keep a block in place with your hand behind it, put the treadmill on high, and gradually slide it to the side off the treadmill.

You won't feel any forward momentum propelling is forward. Empirical evidence...End of thread.

No momentum.

To make this a better analogy to running imagine a small RC car on the treadmill. It is moving forward under its own power. If the belt suddenly stopped and you at the same instant turned off the power to the car, the car would continue moving forward on the belt. This is because it has momentum relative to the belt.

I think this discussion is omitting a key variable between roads and treadmills. When your shoe hits pavement, there is no compression of road. It does not give. When your shoe hits the belt of a treadmill, even a stiff treadmill, the surface gives. Then it rebounds. I've never done this, but I'd guess that if you stood in the middle of a stopped belt, jumped up and landed hard, the belt would oscillate up and down a couple of times before returning to the neutral position.

It wouldn't take much give to change the dynamics of the energy stored in the tendons or the energy of the push off. For example, let's assume that the push off exerts downward force on the belt, and the belt gives downward a little due to the push off. That energy is now lost.

Conversely, if the belt oscillates and the belt's movement is up at the moment of push off, it might add to the stride. I have noticed this effect on some non-commercial treadmills. On one Nordic track treadmill, I could hit a harmonic pace where I could almost bounce along on the treadmill.

This female runner, like many runners, does most of her runs on a treadmill and she ran a 2:35:02. Forget the BS running is running.

http://runningtimes.com/Article.aspx?ArticleID=21039

Demotivator wrote:

To make this a better analogy to running imagine a small RC car on the treadmill. It is moving forward under its own power. If the belt suddenly stopped and you at the same instant turned off the power to the car, the car would continue moving forward on the belt. This is because it has momentum relative to the belt.

The car would move forward, but only because some of the rotational momentum in the wheels and drive train would provide a force to accelerate the rest of the car. In the off-treadmill inertial frame the rest of the car doesn't have any velocity and hence zero momentum to make it move in that reference frame unless force is applied.

If you had a skateboard on a string fixed to the front of the treadmill and a second skateboard sitting on top of the first skateboard, then when the treadmill stops the bottom skateboard would roll forward out from under the top skateboard. We're assuming skateboards with frictionless wheel bearings and wheels with non-zero mass.

Ok fair enough.. running is running, but on to the bigger question, how could an airplane possibly take off?

I don't think you understand physics very well. Just because you don't have a net loss in elevation, doesn't mean you are not scrubbing off potential energy during the whole run. You are, it is just being replaced by a different source (the treadmill motor). For example, on every stride, you land in front of (and lower than) where you pushed off (a decrease in potential energy), and then the treadmill "replaces" that potential energy while your leg is in contact with the belt, at which point you push off again and the cycle repeats.Another way to think about it is if you run down a hill, and then ride an elevator back up to the top. You can't say that you didn't just run downhill, because your energy level is the same as when you started, can you? Running downhill on a treadmill is akin to that, except you take a (very short) elevator ride every stride.Now, I am not saying that the exact energy expenditure is the same, because some of the running mechanics clearly change. However, the assertion that you don't change potential energy during a hill run on a treadmill is incorrect.

lucKY2b wrote:

The difference is that treadmills are not a replacement for doing hills. When you run downhill, you are actually lowering your gravitational potential energy, hence it feels easy to pick up momentum. You don't get that effect on a treadmill (no change in elevation). Opposite is also true for running uphill. It costs you energy to raise your body up some physical elevation, something the treadmill can't do. That's not to say that it doesn't cost you more energy to run with the treadmill at an incline, it just shouldn't be equated with running the same incline hill.

Thanks. I think I was conflating the first few steps with after you've adapted to the treadmill belt. As in, thinking that if you could make something that bounced perfectly, approaching 0 contact time or lost energy, and dropped it on a treadmill, it could continuously bounce in place (relative to the room) while the belt ran underneath it. Obvs this isn't the right way to think about it.

Here's my take on why running on a treadmill is different (the main reason):

Your brain governs your location with respect to both the belt and the room. In other words, your brain doesn't let you hit the front of the treadmill or the side handrails. This is different than running, because you will sometimes slow down (use a muscle for braking) to shift yourself farther from the front of the treadmill, when on the open roads, you would never do this. This meshes with my experience of having very sore hips after getting on a treadmill for three hard runs in a row after not being on a treadmill (but running every day) for years.

frame of reference wrote:

Everything is relative. Relative to the belt, you have "forward" momentum. The ONLY difference at a constant speed is there is no wind resistance on the treadmill. But this is a pretty big difference.

It actually isn't. Many studies have tried to "simulate" outdoor running on a TM by changing the grade and figuring out what %grade is metabolically equal to running over-ground.

Depending on which paper you want to cite, level (0%) grade is simulated anywhere between 0-2% grade on a treadmill. This primarily depends on the speed at which you're running since air resistance is a function of velocity squared. However, we have also found that running on a treadmill costs "extra energy" compared to over ground running, primarily due to the extra energy required for cooling. Your metabolic cost is slightly elevated because of the material properties of the TM belt, which has a tendency to elevate the vertical oscillations of your center of mass compared to over ground. This energy is over and above the extra energy you might save by having a more elastic surface, thus conserving energy as elastic potential energy in your tendons.

Contrary to one a previous poster said, you CANNOT simulate wind resistance on a TM by using a fan since you are not moving forward relative to the air flow of the fan...your body doesn't require any extra energy to "run into" the wind created by the fan. In fact, running into a fan almost completely eliminates the added metabolic cost of treadmill running as a result of increased cooling.

[quote]Physics Minor wrote:

I don't think you understand physics very well. Just because you don't have a net loss in elevation, doesn't mean you are not scrubbing off potential energy during the whole run. You are, it is just being replaced by a different source (the treadmill motor). For example, on every stride, you land in front of (and lower than) where you pushed off (a decrease in potential energy), and then the treadmill "replaces" that potential energy while your leg is in contact with the belt, at which point you push off again and the cycle repeats.

Another way to think about it is if you run down a hill, and then ride an elevator back up to the top. You can't say that you didn't just run downhill, because your energy level is the same as when you started, can you? Running downhill on a treadmill is akin to that, except you take a (very short) elevator ride every stride.

Now, I am not saying that the exact energy expenditure is the same, because some of the running mechanics clearly change. However, the assertion that you don't change potential energy during a hill run on a treadmill is incorrect.

[quote]

Sorry, but you are absolutely wrong on this. Change in gravitational potential energy IS mgy_f-mgy_i. If y_f = y_i, there is no net change in gravitational potential energy and you've not done work against gravity; end of story. Any additional energy expended while the treadmill is inclined is just because you do need to lift your knees a little higher, and you do cut off your stride on the back end a little, but that's it. If you were taught differently, you were misinformed.

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