Treadmill Physics Questions (Similar to Airplane Question)

before I reply about poor quality treadmills....

a paper from late 2009 is quite interesting.

http://www.ncbi.nlm.nih.gov/pubmed/19683240?dopt=Citation

here is the abstract:

J Biomech. 2009 Nov 13;42(15):2569-74. Epub 2009 Aug 15.

The consistency of maximum running speed measurements in humans using a feedback-controlled treadmill, and a comparison with maximum attainable speed during overground locomotion.

Bowtell MV, Tan H, Wilson AM.

Structure and Motion Laboratory, Royal Veterinary College, London, UK.

mbowtell@rvc.ac.uk

Abstract

Consistent measurement of maximum running speed overground is problematic due to the difficulty in precise, continual measurement of speed, and the substantial workload in accelerating the body promoting the onset of fatigue. Treadmills remove the requirement for acceleration which enables more repeats. They also allow experiments to be carried out in controlled environments and where space is limited, but they usually depend on manual and subjective speed control. Here we used a draw-wire position sensor and a proportional-derivative (PD) controller to automatically adjust treadmill belt speed of a large equine treadmill. The feedback loop took the real-time position and velocity of the runner relative to the front of the treadmill as input. This control system allowed runners to accelerate from walking speed to a peak running speed within a few strides and then decelerate as quickly as they wished. We used the system to evaluate the variation in maximum speed determination that results from one trial to 10 trials, in eleven individuals. Three trials gave a maximum speed 97.8% of that achieved after ten. The approach used is appropriate for any treadmill where the running zone length is greater than three metres and the speed controller can be externally controlled. Subjects ran 11.5% faster on the treadmill than overground, part of which can be explained by the removal of aerodynamic drag and the fatigue of overground running. Additional factors may, however, contribute to athletes running faster on a treadmill, for instance some aspect of stability or control.

This thread began with a mention if inertia.

This servo treadmill allows acceleration up to sprint speeds without the impeding inertial force. As you can read, this allowed the runners to reach faster maximum speeds. Their reasoning (which I agree with) is that the metabolic energy used for acceleration overground is spared and thus a faster top speed is reached. Aerodynamic drag also probably does play a more significant role at these speeds.

re: speculation about whether a poor quality treadmill with large belt speed fluctuations would make running more or less costly.

I can't say for sure. We have talked about removing the flywheel from our treadmill and measuring belt speed fluctuations. If we ever do it, we could measure VO2 also. But there has not been a high motivation for us to do that experiment. If you jack up the back of your gym treadmill so that you are running downhill, you can bog down the motor pretty easily. I would be curious as to what the speed readout is under those conditions. i.e. if you set it to 8MPH and you run downhill and bog the motor, does the read out still say 8 MPH? Have a friend time 10 belt revolutions with a stop watch and a piece of tape and compare the time to 10 revs during level running with the 8MPH setting. Compare the time for 10 belt revs with a lightweight and a heavyweight runner. Meanwhile, I'll be out running on the trails. ;-)

hoppity skip wrote:

OP: you are whiny bitch. who complains about not having enough inertia and thus having a harder time turning?? haha ths is pathetic, stop overanalyzing shit and just run.

Who complains? who complains? Andrew Wheating complains about running indoor track because the narrow turns don't suit a tall guy like him. Im not all that tall but something about my running style build gives me a similar feeling. And that does have to do with inertia.

p.s.

I hope the mods don't remove my thread for failing to call someone an idiot or a d-bag.

I'm sorry for not following LR standard practices.

Yeah, well i guess in this situation I wouldn't be stutter stepping every few minutes to avoid the side, the front, or going off the back of the belt. I guess just the size of the belt plays a factor in while my form feels cramped or why i end up landing strange. i think my speed varies a fair amount when i am on a run outside. even if overall i am speeding up the whole time, i think i gradually speed up, slow down, then speed up. nothing noticeable but having the constant speed on the treadmill might throw off my gait.

Sprint Geezer wrote:

These non-laboratory-grade treadmills no doubt measure distance travelled simply as a mathematical function of the programmed speed, and not as a function of the distance actually travelled by the belt.

Does anybody know if that is true?

I once did a short recovery run on a hotel treadmill. I don't recall the exact numbers, but for simplicity's sake, let's say it was 6 mph for 30 minutes (so you'd expect a 3 mile run). After the 30 minutes the odometer on the treadmill read something like 2.4 miles. I get that the speed calibration is unreliable but found it bizarre that the speed and distance claimed by the treadmill was not self consistent.

I've used treadmills where the belt noticably slows when your foot impacts the belt, due I suppose to friction between the belt and the plate underneath it. The effect on form is, I think, similar to a very pronounced overstride.

A bunch of interesting things:

I wasn't aware of the existence of equine treadmills...a whole new world!

The abstract doesn't mention the duration required of the maximum speed--if it was essentially instantaneous, then the lack aerodynamic drag may well account for much of the 11.5% increase on the treadmill, as top speeds would be around 25mph. I find it difficult to believe that it was actually top speed, however, as the abstract mentions that attainment of that speed was achievable "within a few strides" from walking speed. The result is still surprising to me, however.

I don't know that results based on measurement of the result of a maximal effort can be generalized to the results of a sub-maximal effort--there seem to me to be more factors that could affect the sub-maximal effort, leading to a greater variability than in a maximal effort.

I'm going to try your suggested downhill running protocol on our treadmills, hopefully I'll be able to get some results before security intervenes.

Well, a strange thing happened on the way to the forum:

I was able to do the 3 miles at 10 mph, and it seemed easier than it did to do it at 9 mph!!!!!!!

I am not in substantially better shape, & I did not just drop 20 lbs.

I guess 9 mph is just too slow for me, and is somehow inefficient and artificially fatiguing, so actually required as much or more work than running at 10 mph.

The natural question, then, is why the heck was I running at 9 mph and not 10 mph or higher? The answer is that I'm not a distance guy, so I started out at 8 mph a while back, and have been increasing my speed in increments, leading to 9 mph.

Of course I did intervals at 15 mph, but never at 10 mph, and therefore I never realized that 10 mph is easier than 9 mph.

It is also totally counter-intuitive. When laboring at 9 mph, who the heck would RAISE the speed to 10 mph?

Heck, next time I'm going to try 10.5 or 11 mph.

Maybe that's the difference: when running freely, you can settle into whatever pace is comfortable, almost instantly. When speed is constrained on a treadmill and the response time is long, you don't "settle" into a good pace at all--you have to have some idea of what is a good pace for you to begin with, and set the treadmill accordingly.

This is probably no revelation at all to endurance runners, but to a hack like me, when it is zero fahrenheit outside and a treadmill is readily available, it is an epiphany.

BTW, regarding footfall and retarding of the belt: I burned out our True treadmill, which was the only one that went to 15mph. The thermal breaker now trips any time it gets going reasonably fast. Talk about a drag!

Sprint Geezer:

Sorry, but I can't post the whole servo-treadmill article here due to copyright regulations.

If you e-mail me directly I can send you a personal copy.

I've never run on this type of treadmill, but it would be intriguing.

Thanks Rodger. Our U has a subscription to J Biomech--I think I'll look up the article, as I have to go tomorrow to do some other research anyway.

Sprint Geezer wrote:

I wasn't aware of the existence of equine treadmills...a whole new world!

.

You really didn't think those race horses were dumb enough to run outside in a foot of snow did you???

Yep, once you include acceleration you're no longer in an inertial reference frame and my analogy doesn't work anymore (hence treadmill running is no longer comparable to overground running).

Uncle Rico & Citizen Runner,I know this was an older post but I was away with some health issues with an elderly parent and couldn't respond earlier. After reading some of the posts, I realize I don't have the physics background as many but your explainations were interesting and please bear with me for further explaination. I understand what you two are saying about relative movement and the perception depends on your frame of reference. The man running 1000mph will run that distance and speed to another person on Earth regardless of the speed of rotation but to someone on the sun his movent will depend on the Earth's rotation. I also understand that movement is defined as between two objects and the stationary object and the moving is relative to your frame of reference.But I think your application to the problem of the runner having the same momentum on the road and treadmill is wrong. (Lets assume we are not including any momentum from feet moving forward on the treadmill) Lets go back to the block analogy which is simple and straight forward. If the block had momentum and you abrutly stopped the belt, the block would slide forward, but it doesn't. (And that would be true regardless if you are on the belt or not) Why?Your thought experiment with relative movement and momentum might be true if they were in outer space and were the only factors. The reason the block doesn't move forward is because the important frame of reference for the block and the OP (the runner) is the Earth. The reason it should be the Earth is because the major force the runner must over come is gravity. The runner on the treadmill has no momentum in the relation to the Earth to help them over come gravity. The runner on the road does move in relation to the Earth and has momentum to help him over come gravity.

Conundrum wrote:

If the block had momentum and you abrutly stopped the belt, the block would slide forward, but it doesn't. (And that would be true regardless if you are on the belt or not) Why?

Your thought experiment with relative movement and momentum might be true if they were in outer space and were the only factors. The reason the block doesn't move forward is because the important frame of reference for the block and the OP (the runner) is the Earth. The reason it should be the Earth is because the major force the runner must over come is gravity. The runner on the treadmill has no momentum in the relation to the Earth to help them over come gravity. The runner on the road does move in relation to the Earth and has momentum to help him over come gravity.

There is no such thing as an "important" frame of reference. All motion is relative and the physics must be equally well described in any inertial reference frame. An inertial reference frame is one that is moving with a constant velocity. The problem is that when you stop the treadmill, you are changing the velocity of the reference frame. It is not an inertial reference frame in that case, and you can't apply your reasoning. You could equally imagine (in a thought experiment) increasing the rotation of the Earth below the treadmill until it matches the speed of the top belt on the treadmill (the whole treadmill itself, of course, is now in motion relative to this new Earth), now what happens when you stop the belt on the treadmill?

lucKY2b wrote:

There is no such thing as an "important" frame of reference. All motion is relative and the physics must be equally well described in any inertial reference frame. An inertial reference frame is one that is moving with a constant velocity. The problem is that when you stop the treadmill, you are changing the velocity of the reference frame. It is not an inertial reference frame in that case, and you can't apply your reasoning. You could equally imagine (in a thought experiment) increasing the rotation of the Earth below the treadmill until it matches the speed of the top belt on the treadmill (the whole treadmill itself, of course, is now in motion relative to this new Earth), now what happens when you stop the belt on the treadmill?[/quote]

In your thought experiment the belt is not in movement in relation to the earth because the Earth is rotating at the same speed. The treadmill frame is in movement in relation to the earth. If you stop the belt the block still doesn't move. that's the way I see it.

The reason I said the Earth frame of reference was so important is that when the runner runs the greatest force to overcome is gravity.

I guess I'm not quite sure what you are doing with the block. Is tethered from the treadmill frame? If so, that is yet another reference frame. I'm thinking of a runner on the treadmill. When the Earth's rotation changes to match the top belt on the treadmill, the runner develops momentum relative to the Earth's frame, not on his accord, but because of an acceleration of the Earth's reference frame. That's my point.

I don't understand the point about gravity. A runner on treadmill is in the same gravity field that he would be if he were standing next to the treadmill.

Unless we're talking about Sunita Williams in which case you'd need glorified bungee cords to simulate gravity:

http://www.youtube.com/watch?v=qbfX2vQaVew

As another thought experiment in reference frames, consider one of those moving walkways like you might find in a large airport. Walking briskly on the moving walkway is exactly the same as walking on a stationary surface. The transition from stationary surface to the walkway and back requires a different stride/balance not because your momentum has changed so much as because your momentum relative to the walking surface has changed.

The point about gravity is that regardless of whether you are on the treadmill or running off the treadmill it is the biggest force you need to overcome. The source of that gravity is Earth. If you have momentum in that frame of reference, Earth, running will be easier. If you are not moving in the frame of reference of earth (the treadmill) then you will not have momentum to help reduce the effects of gravity.

That is why in the real world the block does not slide forward when the belt stops. The treadmill has no movement and therefore no momentum in the frame of reference of the Earth which is the source of force which the runner must overcome.

Conundrum wrote:

The point about gravity is that regardless of whether you are on the treadmill or running off the treadmill it is the biggest force you need to overcome. The source of that gravity is Earth. If you have momentum in that frame of reference, Earth, running will be easier. If you are not moving in the frame of reference of earth (the treadmill) then you will not have momentum to help reduce the effects of gravity.

That is why in the real world the block does not slide forward when the belt stops. The treadmill has no movement and therefore no momentum in the frame of reference of the Earth which is the source of force which the runner must overcome.

No, your reasoning is not correct. Gravity is a field that surrounds Earth and points radially inward towards Earth's center. This field produces a force that is directed inward and is certainly one force that we always have to deal with when discussing motion near the Earth's surface. Unless the object of interest is orbiting Earth or in free-fall, there are likely other forces acting as well: typically a normal force pointing perpendicular to whatever surface your object is on, and some friction force pointed parallel to the surface the object is on. There maybe other forces (like air resistance) as well, but Newton's 2nd Law always applies, which basically says that the net change in momentum the object experiences per unit time is the direct result of a net force acting on the object. This net force is a vector sum (in one dimension, that means adding up forces in one direction and subtracting off forces in the other, in more dimensions it's a little more complicated) of all the forces acting on the object, gravity or otherwise. So gravity is just one of several forces acting and how it acts has no dependence on the velocity of the object. The ONLY thing that matters is if one tries to change the object's momentum (i.e.-accelerate) with respect to a given inertial reference frame. The net force (and its resulting acceleration) is one thing that all observers will agree upon, regardless of what inertial reference frame they are in.

Not sure if that clarifies, but the main point is that gravity is just a force that has a specific magnitude and direction. How it affects (i.e.-accelerates) an object doesn't depend on the object's motion relative to the field. It always produces a force the is mg directed inward, where m is the mass, and g is the strength of the gravitational field (note: g=9.8m/s^2 near Earth's surface).

I can see your point about gravity working the same regardless of the objects motions relative to the field.I am going to grant that I most likely am rigidly fixed on a certain perception and belief that I can not change.No one has convinced why the block on the treadmill wouldn't continue to move if the belt was stopped abrutly when it has the same momentum.

lucKY2b wrote:

So gravity is just one of several forces acting and how it acts has no dependence on the velocity of the object. The ONLY thing that matters is if one tries to change the object's momentum (i.e.-accelerate) with respect to a given inertial reference frame. The net force (and its resulting acceleration) is one thing that all observers will agree upon, regardless of what inertial reference frame they are in.

Not sure if that clarifies, but the main point is that gravity is just a force that has a specific magnitude and direction. How it affects (i.e.-accelerates) an object doesn't depend on the object's motion relative to the field. It always produces a force the is mg directed inward, where m is the mass, and g is the strength of the gravitational field (note: g=9.8m/s^2 near Earth's surface).