## Main Question or Discussion Point

I'm a freshman in college; I took AP Physics C: Mechanics last year in high school. Today my roommate and I got in an argument over whether or not it is easier to run on a treadmill than on flat ground. My friend argues that since the treadmill is moving underneath you, you don't need to exert as much horizontal force on it so it's easier. I argue that when you're running at constant velocity with ideal form, you don't exert any horizontal force on the ground (except for a slight force to counteract air resistance). My roommate said I was retarded and that when we run on the ground, we obviously exert a horizontal force to propel ourselves forward. He says it's biomechanics, and we can't just treat ourselves like blocks. He cited many sources, including a page made by a physics professor. I'm at least 99% confident that I'm right, and yet this guy with a Ph.D says you have to exert a force at a 45 degree angle to the ground with each stride.

Am I right while this professor is wrong? If I am wrong, please explain why.

Thanks.

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DaveC426913
Gold Member
Re: Another treadmill thread: am I more correct than a physics professor?

There are some tricky issues here. A treadmill is not frictionless. It is tilted up so that you work against gravity. That may confound your experiment. You need to clarify with your friend how this treadmill is working. I'll hazard that this is very likely the root cause for your disagreements.

Let's assume a treadmill that is level and under power at exactly walking speed. Does you friend agree with this? You should not assume your friend sees the treadmill experiment having the same setup.

However, allowing for the possibility that you two are both on the same page...

I'm a freshman in college; I took AP Physics C: Mechanics last year in high school. Today my roommate and I got in an argument over whether or not it is easier to run on a treadmill than on flat ground. My friend argues that since the treadmill is moving underneath you, you don't need to exert as much horizontal force on it so it's easier. I argue that when you're running at constant velocity with ideal form, you don't exert any horizontal force on the ground (except for a slight force to counteract air resistance). My roommate said I was retarded and that when we run on the ground, we obviously exert a horizontal force to propel ourselves forward. He says it's biomechanics, and we can't just treat ourselves like blocks.
I would be interested in putting your friend in a darkened warehouse and have tell me how he knows he is on a treadmill and stationary wrt the warehouse walls, or not on a treadmill and in motion wrt to the warehouse walls.

Newton and Einstein would also be interested in his findings.
He cited many sources, including a page made by a physics professor. I'm at least 99% confident that I'm right, and yet this guy with a Ph.D says you have to exert a force at a 45 degree angle to the ground with each stride.

Am I right while this professor is wrong? If I am wrong, please explain why.

Thanks.
This paper mentions absolutely nothing about treadmills versus ground. Everything in that document applies equally to both ground and treadmill. It is totally irrelevant in helping answer the question.

The fact that your friend is citing it actually suggests he is confused about frames of reference. He is probably trying to calculate energy consumption from a stationary point in both cases (on ground, distance covered versus on treadmill, no distance covered). This could be misleading.

All you need do to stop him in his tracks is ask him to examine the darkened warehouse scenario I mention above. There is nothing he can do to determine of he is in motion or not (since even "in motion" is a relative concept), thus there is no difference in exertion.

Alternately, next time your friend is at an international airport, have him ride one of the long people movers. Does he think it requires more effort to walk on a moving people mover than on flat ground? Why?

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Re: Another treadmill thread: am I more correct than a physics professor?

I suggested the airport walkway scenario to him, but he still persisted. The fact that motion is relative should be enough justification, but it wasn't enough for my roommate.

This paper mentions absolutely nothing about treadmills versus ground. Everything in that document applies equally to both ground and treadmill. It is totally irrelevant in helping answer the question.
When we started drawing FBD's I realized the force that a runner exerts on a ground is (ideally) vertical unless the runner is stopping or starting. My roommate disagreed with this conjecture, but seemed to acknowledge that IF the force is only vertical, it would be impossible for the treadmill to "help" the runner. So he found a source that contradicted my idea.

If we put my roommate out of the picture, there is still a disagreement between Professor Sprott and me. The linked source says,

"For the running case, the force is impulsive (it occurs over a very short time interval), and it is thus much larger than the person's weight. Furthermore, to launch the person at a 45° angle requires equal vertical and horizontal forces." (it's under "friction requirements")

He's saying that a horizontal force is required to propel a runner forward with each stride. I remember this is how my physics teacher taught us (though it was a qualitative example), and I say it's wrong. Is the accepted model for running one that agrees with my physics teacher and Prof. Sprott? If so, it's WRONG!

Thanks for your reply, and as a side note, why is a treadmill tilted up? Wouldn't a horizontal surface be closest to the experience of running on flat ground?

DaveC426913
Gold Member
Re: Another treadmill thread: am I more correct than a physics professor?

I suggested the airport walkway scenario to him, but he still persisted. The fact that motion is relative should be enough justification, but it wasn't enough for my roommate.

When we started drawing FBD's I realized the force that a runner exerts on a ground is (ideally) vertical unless the runner is stopping or starting. My roommate disagreed with this conjecture, but seemed to acknowledge that IF the force is only vertical, it would be impossible for the treadmill to "help" the runner. So he found a source that contradicted my idea.

If we put my roommate out of the picture, there is still a disagreement between Professor Sprott and me. The linked source says,

"For the running case, the force is impulsive (it occurs over a very short time interval), and it is thus much larger than the person's weight. Furthermore, to launch the person at a 45° angle requires equal vertical and horizontal forces." (it's under "friction requirements")

He's saying that a horizontal force is required to propel a runner forward with each stride. I remember this is how my physics teacher taught us (though it was a qualitative example), and I say it's wrong. Is the accepted model for running one that agrees with my physics teacher and Prof. Sprott? If so, it's WRONG!
What I don't understand is why - regardless of what forces are required or invoked - it would be any different between ground and treadmill.

When we do calculations in a spaceship travelling to Mars, do we determine the forces relative to Earth? The whole point of inertial motion is that it is not relevant with the system (runner and ground) what the walls of the warehouse happen to be doing.

Thanks for your reply, and as a side note, why is a treadmill tilted up? Wouldn't a horizontal surface be closest to the experience of running on flat ground?
Treadmills are not designed to mimic running; they are designed to provide a workout.

Wouldn't it be a simple matter of adding vectors? I'm not sure if that's what you guys mean, but just throwing otu the forces argument. If you have a velocity vector against you (the treadmill) vs not having one, then it should naturally be harder to go at the same speed with the treadmill. Or am I missing something here?

Re: Another treadmill thread: am I more correct than a physics professor?

What I don't understand is why - regardless of what forces are required or invoked - it would be any different between ground and treadmill.

When we do calculations in a spaceship travelling to Mars, do we determine the forces relative to Earth? The whole point of inertial motion is that it is not relevant with the system (runner and ground) what the walls of the warehouse happen to be doing.
Well duh; you are correct that there would be absolutely no difference. My dumb roommate just hasn't come to that level of understanding. His current argument is that people (i.e. runners) don't behave like idealized blocks. I tried to explain that the laws of physics use the word "body" because the object could be anything - not just a block. Nevertheless, he insists that there's something about humans that makes the laws of physics apply differently, that the motion of the humans legs and arms somehow changes the effect of a force. Obviously he's wrong, but I've moved on.

Now I'm more concerned that millions of physics students are being taught incorrectly—that each stride a person takes requires forward force.

DaveC426913
Gold Member
Re: Another treadmill thread: am I more correct than a physics professor?

Well duh; you are correct that there would be absolutely no difference. My dumb roommate just hasn't come to that level of understanding. His current argument is that people (i.e. runners) don't behave like idealized blocks. I tried to explain that the laws of physics use the word "body" because the object could be anything - not just a block. Nevertheless, he insists that there's something about humans that makes the laws of physics apply differently, that the motion of the humans legs and arms somehow changes the effect of a force. Obviously he's wrong, but I've moved on.
I don't see what idealized blocks have to do with anything.

Now I'm more concerned that millions of physics students are being taught incorrectly—that each stride a person takes requires forward force.
It does. Walking is essentially controlled falling. It requires static friction with the ground to move your CoM forward. This is easily demonstrated every time you try to walk on a sheet of ice. If you cannot apply a forward force, you go nowhere.

Wouldn't it be a simple matter of adding vectors? I'm not sure if that's what you guys mean, but just throwing otu the forces argument. If you have a velocity vector against you (the treadmill) vs not having one, then it should naturally be harder to go at the same speed with the treadmill. Or am I missing something here?
When you're going on a treadmill, you're not trying to move with any speed relative to the rest of your surroundings. Speed is measured relative to the treadmill's belt.

Suppose you're on one of those moving walkways at an airport, and you're walking or running in the opposite direction. Then you would obviously lose in a race against someone that's not on the walkway. In that situation, the person on the walkway would have a velocity vector working against them, but in the case of a treadmill the velocity vector is moot.

Treadmills can be but are not necessarily tilted up. They are adjustable. The tilt allows you to run uphill and stress your cardiovascular system more which running on a level surface does not do to any great degree because you aren't lifting your own weight with each stride to any great degree.

When running you have to consider two things - the motion of your center of mass and the motion of your legs. Let's suppose you are suspended so your feet touch the treadmill or the ground but there is no need to launch yourself into the air when you run. Exactly what force do you have to exert in each case, on a sidewalk and on a treadmill? Once you initially accelerate and are moving at a constant speed in a straight line, all you have to do is move your legs backwards and forwards like a pendulum to simulate the running but do you have to push? No. Because you are moving at constant speed once you begin and will continue to travel at constant speed. So you just move your feet back and forth in either case so you don't trip or something but you have no force to exert.

So now let's run without being suspended. Yes you launch at what appears to be an angle but actually in what direction do you exert the force? Vertically. It looks like an angle because you already have forward motion and when you combine a vertical jump with a forward velocity it looks like the force was exerted at an angle when it actually was not. Consider that you are running and suddenly hit a completely friction free surface. Can you still run? You can. Because you can exert a vertical force on a friction free surface and you are already moving forward at a constant speed and will continue to do so unless you can slow because friction is now available or you run into a wall or something. If the runner is exerting a backward force so that friction is pushing the runner forward, the runner would continue to acceleration rather than run at constant speed. Now in the real world one would have to exert a small backward force because of friction and the fact that one doesn't move at a perfectly constant speed and when the runner lands on one leg, he probably does slow a small amount. But not a lot. The main energy consumption is going to be the force needed to launch the person vertically through the air to the next landing point where his already existing velocity will take him, not from any small forward force needed to smooth the motion because of landing and launching irregularities. I see no way the horizontal and vertical components of the force would be close to equal. And considering the fact that the earth is really a treadmill and is moving under us at the rate of one circumference every 24 hours at the equator if we were able to stay motionless relative to a motionless earth not spinning. I see no difference whatsoever in a mechanical treadmill and the earth treadmill.

Re: Another treadmill thread: am I more correct than a physics professor?

It does. Walking is essentially controlled falling. It requires static friction with the ground to move your CoM forward. This is easily demonstrated every time you try to walk on a sheet of ice. If you cannot apply a forward force, you go nowhere.
But once you start moving, it's not hard to keep moving. I believe it's harder to walk on ice because we rely on the friction for stability, not propulsion. Consider this question: what happens to all the force when you're walking on ground? Wouldn't you be constantly accelerating?

The way I see it, in the case of walking, most people exert a breaking force when their foot touches the ground, and an equal (neglecting air resistance) propulsive force when their foot is on the ground (I would speculate that most of it happens as the foot is leaving the ground).

In the case of perfectly efficient running, runners have their leading foot moving back (relative to their bodies) before it touches the ground. The foot touches the ground and doesn't exert a horizontal force. It only exerts an upward force before lifting off the ground.

EDIT:netgypsy beat me to it. Props.

DaveC426913
Gold Member
Re: Another treadmill thread: am I more correct than a physics professor?

But once you start moving, it's not hard to keep moving.
If you were on frictionless ice and somehow managed to get moving - you would keep moving regardless of whether you put any effort into walking. You would simply continue inertially.

i.e. when on a frictionless surface, any effort of walking will not be contributing to your motion.
i.e. on a surface with friction it is the friction that allows you to continue moving.

Born2bwire
Gold Member
You have to provide a forward thrust, otherwise how would you move forward? The only force that would be acting would be gravity which pulls down. You can move your center of mass forward in your step but the gravitational force will only act orthogonal to your desired direction of travel. You have to provide the force that moves your center of mass horizontally.

I just went out and ran around the block.

It seems to me that there are three stages: a landing stage where you break your fall by bending the leg a bit to absorb the shock, then there's what might be called a "rollover" where inertia carries you forward to the "leap" point, then a "leaping" stage where you propel yourself forward by suddenly straightening the leg and tightening the calf muscle and pushing off with the foot.

To me each "leap" felt like an acceleration, and that there was a horizontal component.

Empirical, anecdotal, I know. But I think the professor has a chance of being right.

When running you certainly push yourself forward, anybody who has sprinted knows how sore the hamstrings become and their role is to pull the leg back.
With the treadmill vs running on ground thing there can't be any difference because if you extended the treadmill band out infinitely and had it move relative to you then your motion in the frame of reference of the band is exactly the same as that from the frame of reference on the ground if you were running without a treadmill.

I think roommate's point about "humans beng different" is that most of the energy we use when walking is not to move forward, but to swing our legs back and forth and lift them up and down. It's very inefficient and he does have a point...

...however, I don't see what difference it makes whether you're on the "still" ground or on a treadmill. Either way you have to swing your legs and lift them up and down if you want to keep relative motion and not fall. I suppose there's air resistance, but it looks like it's been left out of this discussion, and for good reason.

What is it about a treadmill that makes it so special anyway? what if we increase the size of the treadmill...does it cease to act like one at some point? What if the treadmill was replaced by a huge spinning ball...the size of the earth perhaps. Would it make a difference whether you're on it or on the earth itself? Would it make a difference if you try to go one way or another?

On a side note, be wary about arguing with "highly educated" people. They can start with the assumption that their education makes them right, and it can make the argument impossible to win.

russ_watters
Mentor
You have to provide a forward thrust, otherwise how would you move forward? The only force that would be acting would be gravity which pulls down.
Note that once you are moving, Newton's 1st law demands that all horizontal forces sum to zero. So the only net/external forward force you provide is against wind resistance.

The vast majority of the energy expended while walking or running is in supporting (or bouncing!) yourself against gravity. And the longer your stride, the lower the angle and therefore the greater the force.

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Try this one (assuming the treadmill is level).
The earth is rotating under our feet at about 1000 mph (actually less in a US/European latitude), west to east, just like a treadmill. So is it easier to run east or west?

And no, gravity does not pull you along the surface of the earth, it only pulls you down against it, just like the treadmill.

AlephZero
Homework Helper
The work done to overcome air resistance is not negligible.

Using the standard formula $F = C_p \rho a V^2 / 2$

$C_p$ is about 1.0 for a not-very-streamlined shape like a human. I'm estimating the frontal area as about 0.8 $m^2$. At 5 m/s (i.e 100m in 20 sec) that gives a drag force of 12N or a power requirement of 60W to overcome air resistance. The maximum power output an average human can sustain for a long period is of the order of 200W.

The power varies as the cube of the velocity, so this estimate would suggest the thing that limits the speed of a sprinter (round about 10m/s) is the work done overcoming air resistance.

The runner probably won't feel the force of 12N (about 3 pounds) as being significant compared with the other forces involved like the impact of feet on the ground.

The work done to overcome air resistance is not negligible.
You might have a tail wind. Air resistance is quite variable and, as mentioned, small compared to the vertical force typically exerted. But if you've ever watched "daisy clipper" runners they have almost no loft so it's pretty much the force needed to move the legs back and forth when running at constant speed and direction that they must exert to keep going.

And yes your professors will make errors. The good ones appreciate being questioned. It means you are paying attention. If they're smart they'll just smile and say "Just threw that in to see if you were watching".

russ_watters
Mentor
The work done to overcome air resistance is not negligible.

... At 5 m/s (i.e 100m in 20 sec) that gives a drag force of 12N or a power requirement of 60W to overcome air resistance. The maximum power output an average human can sustain for a long period is of the order of 200W.

The power varies as the cube of the velocity, so this estimate would suggest the thing that limits the speed of a sprinter (round about 10m/s) is the work done overcoming air resistance.

The runner probably won't feel the force of 12N (about 3 pounds) as being significant compared with the other forces involved like the impact of feet on the ground.
You have a bunch of inconsistencies there, related to the mixing of different speeds. Sure, an AVERAGE human might only put out 200w CONTINUOUSLY, but that's off by about an order of magnitude for a 10 m/s sprinter, particularly when he's accelerating.

An "average" person can't sustain anywhere close to even 5m/s: 3m/s, maybe.

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When running you certainly push yourself forward, anybody who has sprinted knows how sore the hamstrings become and their role is to pull the leg back.
Yes, and the reason you have to push yourself forward is because the "landing" involves some acceleration in the negative direction. You're removing some of your 1st law motion with each "landing" which then is replaced on the "leap". The slower you run, the worse that is, and the faster you run the more 1st law advantage you have in keeping everything above the waist in motion, (while accelerating the legs becomes harder and harder because that has to be done faster and faster).

Re: Another treadmill thread: am I more correct than a physics professor?

He's saying that a horizontal force is required to propel a runner forward with each stride. I remember this is how my physics teacher taught us (though it was a qualitative example), and I say it's wrong. Is the accepted model for running one that agrees with my physics teacher and Prof. Sprott? If so, it's WRONG!
My last post got me thinking. The horizontal force would be necessary because you are accelerating the opposite leg forward essentially horizontally. Since the opposite leg's motion is essentially horizontal, the leg in contact with the ground has to counter it horizontally. While the center of mass is in continuous motion the legs are constantly applying force against their horizontal inertia. Legs have a lot of mass relative to a body. This is not a negligible amount of force at all.

it's just badly stated. The force does not propel the runner, it propels the runners legs only (disregarding air friction and stride irregularities).

You have to accelerate your legs to run and that force is significant to move your legs but you are not propelling the runner, you are propelling the runner's legs. The rest of the body, pelvis upward, is already moving and will keep moving.

This is why, when you trip, you go down face first. Your feet stop because of friction but the rest of you keeps moving forward until friction stops you from moving. Personal experience - a colleague was running down a smooth hall carrying a load of tests for a class. She tripped, fell face first, and slid probably 15 feet before stopping.

If you were on frictionless ice and somehow managed to get moving - you would keep moving regardless of whether you put any effort into walking. You would simply continue inertially.
I was thinking of real ice, not frictionless ice.
i.e. when on a frictionless surface, any effort of walking will not be contributing to your motion.
i.e. on a surface with friction it is the friction that allows you to continue moving.
Unless you're talking about counteracting air resistance, there's no need for a horizontal frictional force when running with good form (with walking it's pretty hard to walk without exerting a significant breaking force, which would mean a propulsive force would be required somewhere in the stride). You would continue inertially until acted upon by a horizontal force. Friction doesn't allow you to continue moving, it allows you to regain speed after it slows you down. The real use of friction when walking or running is stability (and counteracting air resistance).

When running you certainly push yourself forward, anybody who has sprinted knows how sore the hamstrings become and their role is to pull the leg back.
Yes, and the reason you have to push yourself forward is because the "landing" involves some acceleration in the negative direction. You're removing some of your 1st law motion with each "landing" which then is replaced on the "leap". The slower you run, the worse that is, and the faster you run the more 1st law advantage you have in keeping everything above the waist in motion, (while accelerating the legs becomes harder and harder because that has to be done faster and faster).
At speed, the only horizontal force sprinters need to exert is a force to overcome air resistance. Good sprinters won't exert any breaking force when they land. Runners with good form also won't exert a significant breaking force even if they're running at an easy pace.
My last post got me thinking. The horizontal force would be necessary because you are accelerating the opposite leg forward essentially horizontally. Since the opposite leg's motion is essentially horizontal, the leg in contact with the ground has to counter it horizontally. While the center of mass is in continuous motion the legs are constantly applying force against their horizontal inertia. Legs have a lot of mass relative to a body. This is not a negligible amount of force at all.
it's just badly stated. The force does not propel the runner, it propels the runners legs only (disregarding air friction and stride irregularities).

You have to accelerate your legs to run and that force is significant to move your legs but you are not propelling the runner, you are propelling the runner's legs. The rest of the body, pelvis upward, is already moving and will keep moving.
When a runner lifts his knee up after pushing off, the other leg goes back, so the center of mass isn't disrupted. By moving the leg back (not exerting a horizontal force on the ground), the center of mass of the legs (and therefore the entire body) is balanced and it allows everything to move smoothly. If the runners legs were accelerating and his body wasn't, the runner would be broken apart at the torso. The legs would continue increasing velocity, and the torso would plummet to the ground with nothing to support it.

AlephZero is probably right. Having spikes rather than trainers is a big advantage, but only in races where the runners are moving fast (and has to deal with a lot more air resistance). On an easy run, spikes don't help at all except for the difference in weight. My roommate says from experience that running on a treadmill is easier than running outside; this is probably due to air resistance and nothing more.

It's true that when most people run on ice, their foot slips as it pushes off. On a surface with plenty of friction, this "toe off" probably makes up for air resistance, and isn't necessary on a treadmill.

DaveC426913
Gold Member
Unless you're talking about counteracting air resistance, there's no need for a horizontal frictional force when running with good form (with walking it's pretty hard to walk without exerting a significant breaking force, which would mean a propulsive force would be required somewhere in the stride). You would continue inertially until acted upon by a horizontal force. Friction doesn't allow you to continue moving, it allows you to regain speed after it slows you down. The real use of friction when walking or running is stability (and counteracting air resistance).
If this were true (that you don't need to impart a horizontal force to keep moving) then runners could adopt a simple pogo-stick style of running - doing nothing but providing a direct downward force to keep them off the ground.

Go look at the footprints in a wet track. The surface most definitely experiences a strong backward push from the runner.