Runner on a Treadmill

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
Goemon
Posts: 442
Joined: Mon Nov 19, 2007 4:57 am UTC

Runner on a Treadmill

Postby Goemon » Tue Jul 30, 2013 5:04 am UTC

This article purports that measurements of Usain Bolt's world record 100m dash show that 92.21% of the energy he expended during the run were devoted to overcoming drag from air resistance.

Does that imply that he would expend only 8% as much energy to run a 100m dash on a treadmill? (Or maybe a little more for air turbulence due to back and forth motion of arms and legs?) And I've got to wonder how much faster he could achieve 100m without the air resistance... is a runner's top speed really limited by drag from the air or other factors?
Life is mostly plan "B"

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6142
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Re: Runner on a Treadmill

Postby skeptical scientist » Tue Jul 30, 2013 6:07 am UTC

Goemon wrote:And I've got to wonder how much faster he could achieve 100m without the air resistance...

We should totally make him run the 100 meters in hard vacuum and compare.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

User avatar
folkhero
Posts: 1775
Joined: Fri Aug 01, 2008 3:34 am UTC

Re: Runner on a Treadmill

Postby folkhero » Tue Jul 30, 2013 8:30 am UTC

That number seems really wrong to me. I would think that energy going to internal friction inside the body alone would be more than 8%; go out and do some extremely difficult physical activity even if you only do it for 10 seconds you will notice your body temperature rise noticeably What Bolt does in the 100 meter dash is way more physically intense than anything you or I could do. Combine that with energy lost in the impact of shoes hitting track and the actual energy of accelerating mass, and well I'm not doing any actual calculations here but I'm having trouble believing all those things don't even reach 8% of the total energy expended.

I live at an elevation of about 2 kilometers above sea level, which is about 80% the air pressure of sea level. Endurance athletes come hear a lot to train because of the lower oxygen, but I've never heard of short distance races having inflated (or I guess deflated) times because of lower drag. You'd think that athletes would come to high altitudes all the time to try to set records if the effect were that substantial. The shorter the race, the less important the available oxygen in the air is since your largely just using the oxygen already in your body early on. That said, a tail wind has a non-trivial effect on times, and I've seen some video lately of NFL players or prospects running really fast on treadmills, probably quite a bit faster than they would be able to run on a field.

I haven't done any actual calculations, so I might be way off on all of this.
To all law enforcement entities, this is not an admission of guilt...

User avatar
idobox
Posts: 1591
Joined: Wed Apr 02, 2008 8:54 pm UTC
Location: Marseille, France

Re: Runner on a Treadmill

Postby idobox » Tue Jul 30, 2013 9:32 am UTC

folkhero wrote:That number seems really wrong to me. I would think that energy going to internal friction inside the body alone would be more than 8%; go out and do some extremely difficult physical activity even if you only do it for 10 seconds you will notice your body temperature rise noticeably What Bolt does in the 100 meter dash is way more physically intense than anything you or I could do. Combine that with energy lost in the impact of shoes hitting track and the actual energy of accelerating mass, and well I'm not doing any actual calculations here but I'm having trouble believing all those things don't even reach 8% of the total energy expended.

I think most of the energy is lost as heat by the chemical->mechanical energy conversion. That being said, it depends on what you're measuring, the 8% could be of the total mechanical power expanded. IT would be like looking at a car with 30% energy conversion efficiency, and saying that 80% of the actual mechanical power is lost to drag, that would actually be 80% of 30%.

skeptical scientist wrote:We should totally make him run the 100 meters in hard vacuum and compare.

As long as we keep friction... And he might actually perform not that bad, it took him a little bit less than 10s, and he although it would affect his performance, holding his breath that long is very possible, even when running.
Another way would be to move a big plexiglass cage around him, to keep air mostly immobile compared to him.
If there is no answer, there is no question. If there is no solution, there is no problem.

Waffles to space = 100% pure WIN.

elasto
Posts: 3778
Joined: Mon May 10, 2010 1:53 am UTC

Re: Runner on a Treadmill

Postby elasto » Tue Jul 30, 2013 11:09 am UTC

idobox wrote:and he although it would affect his performance, holding his breath that long is very possible, even when running.

My understanding is that some (many?) hold their breath anyhow. I doubt that any oxygen they breath in during the race has the time to have any significant metabolic effect either way.

http://www.viewzone.com/breathing.html

User avatar
The Geoff
Posts: 144
Joined: Wed Jun 08, 2011 6:22 am UTC

Re: Runner on a Treadmill

Postby The Geoff » Tue Jul 30, 2013 11:30 am UTC

Simple solution: rig up a fan to give him a tailwind equal to his velocity.

User avatar
Xenomortis
Not actually a special flower.
Posts: 1456
Joined: Thu Oct 11, 2012 8:47 am UTC

Re: Runner on a Treadmill

Postby Xenomortis » Tue Jul 30, 2013 11:36 am UTC

elasto wrote:I doubt that any oxygen they breath in during the race has the time to have any significant metabolic effect either way.


It doesn't. Sprinting, like any short intense activity, is very much anaerobic.
Image

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 12:05 pm UTC

This is very surprising to me. I know that wind directionality has a fairly large impact on running performance, but the notion that approximately 98% of his energy went into overcoming air resistance just seems very, very off. It was my understanding that a sprinter achieves maximum speed fairly rapidly, within 4-5 strides, and the remainder of the sprint is about maintaining that speed. I would have assumed that a ~160-180 lb sprinters greatest force to overcome was that of inertia.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
Xenomortis
Not actually a special flower.
Posts: 1456
Joined: Thu Oct 11, 2012 8:47 am UTC

Re: Runner on a Treadmill

Postby Xenomortis » Tue Jul 30, 2013 12:07 pm UTC

Izawwlgood wrote:and the remainder of the sprint is about maintaining that speed.

Which is all about defeating air-resistance.
Image

elasto
Posts: 3778
Joined: Mon May 10, 2010 1:53 am UTC

Re: Runner on a Treadmill

Postby elasto » Tue Jul 30, 2013 1:07 pm UTC

Xenomortis wrote:
Izawwlgood wrote:and the remainder of the sprint is about maintaining that speed.

Which is all about defeating air-resistance.

Yeah. Bolt won the Olympics taking 41 strides. If he's reached top speed after 4 strides, that means for 90% of the race all his energy is going into maintaining the same speed. ie. it's all going into overcoming the forces that would slow him down - mostly drag.

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 1:17 pm UTC

elasto wrote:
Xenomortis wrote:
Izawwlgood wrote:and the remainder of the sprint is about maintaining that speed.

Which is all about defeating air-resistance.

Yeah. Bolt won the Olympics taking 41 strides. If he's reached top speed after 4 strides, that means for 90% of the race all his energy is going into maintaining the same speed. ie. it's all going into overcoming the forces that would slow him down - mostly drag.

It's the amount air resistance factors in that surprised me. A runner with a ~10mph tailwind isn't going to run ~50% faster, assuming max speed is ~20mph (are they?). Wind direction has been a big influence on these races over the years; I recall reading that no records had ever been set with a headwind, and evidently, if there is a tailwind of >2m/s, the result is disqualified.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
jaap
Posts: 2094
Joined: Fri Jul 06, 2007 7:06 am UTC
Contact:

Re: Runner on a Treadmill

Postby jaap » Tue Jul 30, 2013 1:31 pm UTC

elasto wrote:
Xenomortis wrote:
Izawwlgood wrote:and the remainder of the sprint is about maintaining that speed.

Which is all about defeating air-resistance.

Yeah. Bolt won the Olympics taking 41 strides. If he's reached top speed after 4 strides, that means for 90% of the race all his energy is going into maintaining the same speed. ie. it's all going into overcoming the forces that would slow him down - mostly drag.


I think most of the energy is going towards waggling his legs back and forth. Most of that is not doing any useful work, and is just to make sure he doesn't fall over. While I can certainly see that more than 90% of the work he does as measured by the horizontal force he exerts on the ground will be to overcome air drag, I do not believe it is really going to be 90% of his total energy expenditure. If he could do it in a vacuum, he is not going to run the same race with a tenth of the effort.

User avatar
davidstarlingm
Posts: 1255
Joined: Mon Jun 01, 2009 4:33 am UTC

Re: Runner on a Treadmill

Postby davidstarlingm » Tue Jul 30, 2013 1:50 pm UTC

Izawwlgood wrote:I would have assumed that a ~160-180 lb sprinters greatest force to overcome was that of inertia.


No, a 160-180 lb sprinter's greatest asset is inertia.

An object in motion will stay in motion unless acted upon by an outside force. That's inertia for you. Recall that work is force multiplied by distance; in the first 4-5 strides, Bolt exerts some force on his body to accelerate it to his peak speed; for the remaining 36-37 strides, he is only exerting force on the air in front of him to accelerate it out of his way. Well, mostly only. There's also heat loss from muscle movement and so on, but that's negligible. Even if the sum force exerted on the air during the last 36-37 strides was just a tenth the force exerted on his body during the first 4-5 strides, it would still represent more than half the energy expended.

However, this doesn't mean that he would be able to run exponentially "faster" on a treadmill. The limiting factor for sprint speed is the force the sprinter can exert on the ground when he "pushes off" with each stride; that's not going to be significantly higher just because there's no air resistance. But he would most likely be able to sustain it for a lot longer.

The thing about a treadmill is that you want to be in contact with it for as short a period of time as possible. In contrast, a sprinter wants to be in contant with the ground almost constantly so he can get the maximum push to slice through the air that is holding him back.

If Bolt ran the 100 meters in a hard vacuum, he'd accelerate for longer, but he'd almost certainly fall. We use air resistance for balance when we're running.

User avatar
idobox
Posts: 1591
Joined: Wed Apr 02, 2008 8:54 pm UTC
Location: Marseille, France

Re: Runner on a Treadmill

Postby idobox » Tue Jul 30, 2013 2:08 pm UTC

What other sources of energy loss are there?
Friction with ground and inelastic deformation are the only ones I could come up with. I have no idea how much power we can loose by deforming our bones and tendons inelastically, but I assume it's rather small. With good shoes, you shouldn't drift much. There is of course deformation of the shoes and track left.
If there is no answer, there is no question. If there is no solution, there is no problem.

Waffles to space = 100% pure WIN.

User avatar
Schrollini
Posts: 515
Joined: Sat Sep 29, 2012 5:20 pm UTC

Re: Runner on a Treadmill

Postby Schrollini » Tue Jul 30, 2013 4:13 pm UTC

I've read the paper, or at least skimmed through it. What they're doing is modeling the forces applied to the runner throughout the race, so the energy budget only includes the center of mass kinetic energy and energy lost to drag. It does not include the energy of moving your arms and legs back and forth, which has to be significant, so don't use these figures for working out how much you need to eat before racing.

Their model assumes that a runner exerts a constant force on the ground, regardless of speed. This seems completely unreasonable to me. When I sprint, I feel like I'm pushing on the ground hard during acceleration, and then just trying to keep my feet from slowing me down for the rest. I would expect that the force falls off significantly with velocity. They justify this approximation by saying:
Jorge Hernandez et al. wrote: Based on the fact that Bolt’s 200 m time is almost twice that for 100 m, our main assumption is that in the 100 m sprint he is able to develop a constant horizontal force F0 during the whole race.

But that doesn't follow at all! All this means is that most of the 100 m is spent at top speed, and this speed can be maintained throughout the 200 m. They follow up on this at the end:
Jorge Hernandez et al. wrote:As mentioned in section 2, a central assumption in our model is that a 100 m sprinter (not only Bolt) is able to develop a constant force during a race (except in the initial few tenths of a second, where he pushes himself against the starting block). To delimit how good this assumption is we use the experimental values of [the velocity] u, the calculated acceleration and the fitted values of the [drag] constants γ and σ to compute F0. The result is shown in figure 4 . It is interesting to note that the average value of the force obtained from this figure is 818.3 N, which is very close to the value obtained from the fitting of the data, 815.7 N.

But all this shows is that their model is consistent; it doesn't show that it is correct! Given that they got the drag forces from assuming this force balance, they have to get this result!

In short, I wouldn't trust these results.

Edit to add: Using their drag coefficients, I get a terminal velocity of about 12.8 m/s for Bolt. Given that a skydiver in the prone position has a terminal velocity on the order of 50 m/s, this suggests that something is wrong.
For your convenience: a LaTeX to BBCode converter

User avatar
davidstarlingm
Posts: 1255
Joined: Mon Jun 01, 2009 4:33 am UTC

Re: Runner on a Treadmill

Postby davidstarlingm » Tue Jul 30, 2013 5:26 pm UTC

Schrollini wrote:I've read the paper, or at least skimmed through it. What they're doing is modeling the forces applied to the runner throughout the race, so the energy budget only includes the center of mass kinetic energy and energy lost to drag.

If that's the case, their "finding" is painfully obvious. "Energy lost to atmospheric drag over 88 meters on a 94-kg man running at 10.4 m/s will be much more than the kinetic energy of that man." No kidding. Kinetic energy is 5.08 kilojoules; for drag energy loss to be equal to kinetic energy, drag force would have to be less than 60 N, only 13 pounds. Anyone who has ever ran anywhere knows that wind resistance is a lot more than just 13 pounds.

Their model assumes that a runner exerts a constant force on the ground, regardless of speed. This seems completely unreasonable to me. When I sprint, I feel like I'm pushing on the ground hard during acceleration, and then just trying to keep my feet from slowing me down for the rest. I would expect that the force falls off significantly with velocity.

Well, the work done should fall off significantly with velocity, but force should be roughly constant.

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 6:46 pm UTC

Again, I'm not a physicist so I'm more than likely not thinking about the kinetics of a runner properly. What surprised me is the extent that air resistance was slowing a runner; I would have imagined that most of a runners energy was expended fighting gravity, since as I understand it, humans are exceptionally efficient runners. Every stride is effectively a small leap forward, and we balance over a center line. To this end, I'd have assumed the biggest energy expenditure was holding ourselves up. I doubt a runner on a treadmill is running 95% more effectively.

davidstarlingm wrote:If Bolt ran the 100 meters in a hard vacuum, he'd accelerate for longer, but he'd almost certainly fall. We use air resistance for balance when we're running.
This doesn't grok with me; you would certainly have to adjust to the lack of air resistance, but... my gut (again, not proof of anything!) tells me that the amount of counter balance air is providing is minimal, hence my surprise that fighting air resistance accounts for ~95% of a runners efforts.

Again, I don't want to make it sound like I'm saying "Well as a runner, I know this is false because I don't feel the air!", I'm just expressing my surprise, based on just gut impressions that this is reported to be the case.

EDIT: To your other point david, about maximizing the time spent with your feet on the ground; I think this is actually the opposite of what sprinters do. All sprinters who have set records toe strike, which minimizes the time their feet spend in contact with the ground. They're landing and immediately bursting off that foot. Number of strides between most sprinters is roughly equal; stride length is the biggest difference you see among sprinters. Usain Bolt is pretty tall, and ripped as hell, but he's not striding faster than other sprinters, he's just leaping further per step.

EDITEDIT: Heh, 'just leaping further'... Heh.

EDITEDITEDIT: http://sciencebasedrunning.com/2011/07/dave/
So you spend about half your time in the air; I guess that makes sense that air resistance is a bigger factor than I assumed.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

DanD
Posts: 335
Joined: Tue Oct 05, 2010 12:42 am UTC

Re: Runner on a Treadmill

Postby DanD » Tue Jul 30, 2013 8:03 pm UTC

I have to agree with what some said above. If the only forces you are counting are due to air resistance and acceleration, then air resistance is going to be the major factor. If you figure out how much energy is lost during leg impact from every stride, then the numbers are going to shift rapidly.

User avatar
Schrollini
Posts: 515
Joined: Sat Sep 29, 2012 5:20 pm UTC

Re: Runner on a Treadmill

Postby Schrollini » Tue Jul 30, 2013 8:12 pm UTC

davidstarlingm wrote:Well, the work done should fall off significantly with velocity, but force should be roughly constant.

I don't buy that.
  1. Try running on gravel. As you accelerate, you'll toss pieces of gravel backwards, but once you're up to speed, you won't. This means the horizontal force you're exerting on the gravel surface must be less than that during acceleration.
  2. Try running on wet grass, compared to dry grass. You'll accelerate more slowly, since the coefficient of friction is lower and the force you can exert before slipping is lower. But you can still reach the same top speed, so the force exerted at top speed must be less than that during acceleration.
  3. Try running with cleats, compared to without. You'll accelerate more quickly, but reach the same top speed. Same conclusion.
  4. By their calculation, the drag force Bolt feels is about equal to his weight. Assuming that the center of drag and center of mass are in about the same place, this means he must be bent forward at 45o for torque balance around his feet. But he and all sprinters stand nearly upright during the cruise section of the race.

Let's look at that linear drag term, which they figure to be dominant. Physically, it would come from Stokes drag, which should only be important at low Reynolds number. But a sprinter will have a Reynolds number of order 105-106, depending on what you take for the characteristic length. Viscous drag should be negligible.

Let's take the spherical Bolt approximation. Treating him as a sphere with radius 0.5m, the Stokes drag in air should be 1.7e-4 kg/s * v. But the coefficient they come up with is 59.7 kg/s -- five and a half orders of magnitude larger! That ain't coming from non-sphericity.

Let's drop the linear term and keep only the quadratic term, which they did show is roughly the right size for inertial drag. This would give us a terminal velocity of 38 m/s. It's a tad slower than we might expect, but it's not so bad.

My conclusion: The drag Bolt feels is roughly 0.6 kg/m * v2, so the energy loss to drag is only about 6 kJ, roughly the same as his kinetic energy. The rest of the "lost" energy never existed, because the force he exerts on the ground decreases with increasing velocity.
For your convenience: a LaTeX to BBCode converter

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 8:37 pm UTC

Schrollini wrote:Try running on gravel. As you accelerate, you'll toss pieces of gravel backwards, but once you're up to speed, you won't. This means the horizontal force you're exerting on the gravel surface must be less than that during acceleration.
This is almost certainly false; you will kick back gravel the entire time you are running, because you are imparting a force on the gravel with each step irrespective of whether or not you are still accelerating or at top speed.
Points 2 an 3 are basically the same; you will accelerate more slowly because some of your rearward momentum is wasted on your foot sliding.

But yeah; most of the energy loss is in maintaining up and down wave like pattern, wherein our arms and head act as counterweights for our legs motion.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
Thesh
Made to Fuck Dinosaurs
Posts: 6598
Joined: Tue Jan 12, 2010 1:55 am UTC
Location: Colorado

Re: Runner on a Treadmill

Postby Thesh » Tue Jul 30, 2013 8:43 pm UTC

Izawwlgood wrote:
Schrollini wrote:Try running on gravel. As you accelerate, you'll toss pieces of gravel backwards, but once you're up to speed, you won't. This means the horizontal force you're exerting on the gravel surface must be less than that during acceleration.
This is almost certainly false; you will kick back gravel the entire time you are running, because you are imparting a force on the gravel with each step irrespective of whether or not you are still accelerating or at top speed.


That assumes that moving your legs back and forth is accelerating you, and not just that you are moving your legs back and forth so you don't fall over, which could very well be the case.
Summum ius, summa iniuria.

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 8:46 pm UTC

Thesh wrote:
Izawwlgood wrote:
Schrollini wrote:Try running on gravel. As you accelerate, you'll toss pieces of gravel backwards, but once you're up to speed, you won't. This means the horizontal force you're exerting on the gravel surface must be less than that during acceleration.
This is almost certainly false; you will kick back gravel the entire time you are running, because you are imparting a force on the gravel with each step irrespective of whether or not you are still accelerating or at top speed.


That assumes that moving your legs back and forth is accelerating you, and not just that you are moving your legs back and forth so you don't fall over, which could very well be the case.
Heh, but you're not running on a 'gravel treadmill'. Every time your foot touches the ground, you are leaping FORWARD. That means imparting not just a downward force on the ground, but also a rearward force.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
Xenomortis
Not actually a special flower.
Posts: 1456
Joined: Thu Oct 11, 2012 8:47 am UTC

Re: Runner on a Treadmill

Postby Xenomortis » Tue Jul 30, 2013 8:55 pm UTC

The force exerted on the gravel will be the same as the force exerted on your due to air-resistance.
This is almost certainly lower, at maximum speed, than it is during the early acceleration phase.

If you were in vacuum, there would be no force, since there would be no change in momentum.
Image

User avatar
Schrollini
Posts: 515
Joined: Sat Sep 29, 2012 5:20 pm UTC

Re: Runner on a Treadmill

Postby Schrollini » Tue Jul 30, 2013 8:58 pm UTC

Izawwlgood wrote:
Schrollini wrote:Try running on gravel. As you accelerate, you'll toss pieces of gravel backwards, but once you're up to speed, you won't. This means the horizontal force you're exerting on the gravel surface must be less than that during acceleration.
This is almost certainly false; you will kick back gravel the entire time you are running, because you are imparting a force on the gravel with each step irrespective of whether or not you are still accelerating or at top speed.

Whether you do or not during cruise will depend on the packing, but I maintain that more will be thrown up during acceleration than cruise, regardless of packing. This is my experience, at least.

Izawwlgood wrote:Points 2 an 3 are basically the same; you will accelerate more slowly because some of your rearward momentum is wasted on your foot sliding.

No, you accelerate more slowly because the maximum tangential force you can apply, given by the coefficient of friction, is less in that case. The runner in flat shoes can accelerate without slipping, but he cannot accelerate as quickly as the runner in spikes can. If they tangential forces during cruise were the same as during acceleration, the runner in spikes would have a faster cruise. But that's not the case. Thus, we must conclude that the tangential forces during cruise are less than during acceleration, at least for the runner in spikes.
For your convenience: a LaTeX to BBCode converter

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 9:09 pm UTC

Schrollini wrote:Whether you do or not during cruise will depend on the packing, but I maintain that more will be thrown up during acceleration than cruise, regardless of packing. This is my experience, at least.
Hmm. I'm having trouble conceptualizing whether or not this is the case. My hunch tells me you're right.
Schrollini wrote:
Izawwlgood wrote:Points 2 an 3 are basically the same; you will accelerate more slowly because some of your rearward momentum is wasted on your foot sliding.
No, you accelerate more slowly because the maximum tangential force you can apply, given by the coefficient of friction, is less in that case. The runner in flat shoes can accelerate without slipping, but he cannot accelerate as quickly as the runner in spikes can.
I'm not trying to be sarcastic here, but I don't see how my statement and yours are different? I was saying that when running on wet grass or without spikes, some of your rearward force is wasted due to your foot slipping, i.e., your maximum tangential force is lower (maybe this is where I'm mixed up?). With spikes, your foot does not slip, and as such, your maximum tangential force is as high as it can be. Since spikes do not increase the max force, only ensure that it does not decrease due to low surface friction, spikes will not increase a runners top speed, only potentially reduce the time it takes to get to top speed.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
Xenomortis
Not actually a special flower.
Posts: 1456
Joined: Thu Oct 11, 2012 8:47 am UTC

Re: Runner on a Treadmill

Postby Xenomortis » Tue Jul 30, 2013 9:13 pm UTC

Izawwlgood wrote:Hmm. I'm having trouble conceptualizing whether or not this is the case. My hunch tells me you're right.

Imagine it on sand. Or that the runner is actually a car.
Image

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Tue Jul 30, 2013 9:37 pm UTC

Xenomortis wrote:
Izawwlgood wrote:Hmm. I'm having trouble conceptualizing whether or not this is the case. My hunch tells me you're right.

Imagine it on sand. Or that the runner is actually a car.
Ah, that does help. Assuming roughly equal output, yeah, I see what he/you mean.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
Schrollini
Posts: 515
Joined: Sat Sep 29, 2012 5:20 pm UTC

Re: Runner on a Treadmill

Postby Schrollini » Tue Jul 30, 2013 10:00 pm UTC

Izawwlgood wrote:I'm not trying to be sarcastic here, but I don't see how my statement and yours are different? I was saying that when running on wet grass or without spikes, some of your rearward force is wasted due to your foot slipping, i.e., your maximum tangential force is lower (maybe this is where I'm mixed up?).

I'm just being a bit pedantic with terminology (force vs. momentum). You are absolutely right that the maximum tangential force is lower; I just didn't see that that's what you were saying!

Izawwlgood wrote:With spikes, your foot does not slip, and as such, your maximum tangential force is as high as it can be. Since spikes do not increase the max force, only ensure that it does not decrease due to low surface friction, spikes will not increase a runners top speed...

They may, though. Consider two runners on ice, one in crampons and one in ballet slippers. I guarantee you that the guy in crampons will have a higher top speed, because the one in ballet slippers will be able to exert so little force that drag will balance this force at a much lower speed than he could otherwise move his legs.

But this isn't what happens with the guy in spikes compared to the guy in flats. Therefore, we conclude that the F(spikes, cruise) = F(flats, cruise) <= F(flats, accelerate) < F(spikes, accelerate). I can't prove that the middle sign is a strict inequality from this argument, but we do know that that last is strict, so the guy in spikes, at least, must exert less force during cruise than during acceleration.

(I think you've already come around on this point, but I'm posting anyway, in case it helps out someone else.)
For your convenience: a LaTeX to BBCode converter

User avatar
davidstarlingm
Posts: 1255
Joined: Mon Jun 01, 2009 4:33 am UTC

Re: Runner on a Treadmill

Postby davidstarlingm » Wed Jul 31, 2013 2:43 pm UTC

Izawwlgood wrote:I would have imagined that most of a runners energy was expended fighting gravity, since as I understand it, humans are exceptionally efficient runners. To this end, I'd have assumed the biggest energy expenditure was holding ourselves up. I doubt a runner on a treadmill is running 95% more effectively.

davidstarlingm wrote:If Bolt ran the 100 meters in a hard vacuum, he'd accelerate for longer, but he'd almost certainly fall. We use air resistance for balance when we're running.
This doesn't grok with me; you would certainly have to adjust to the lack of air resistance, but... my gut (again, not proof of anything!) tells me that the amount of counter balance air is providing is minimal.

I'd argue that the two factors work together. When you sprint, you incline forward; air resistance from air being directed forward and down prevents you from falling onto your face. So almost all the force you exert against the ground goes against air resistance.

I don't want to make it sound like I'm saying "Well as a runner, I know this is false because I don't feel the air!", I'm just expressing my surprise, based on just gut impressions that this is reported to be the case.

Hmm. Let's do a rough estimate. At 50 mph, I can hold my hand out the car window but I experience a fair degree of resistance. With my hand spread open, it's about 20-25 lbs (estimated based on how heavy a 20-25 lb weight feels). Let's say it's 20 lbs.

Bolt sprints at just over 20 mph. At that speed, my hand would be experiencing significantly less drag thanks to the v2 term; only 4.2 lbs. However, my hand has an effective surface area of about 0.02 square meters, while the entire front of my body is around 0.6 square meters. So the total force from air resistance would be around 126 lbs, which is quite significant.

This is a very rough estimate, of course, but 126 lbs is 560.5 N. Over 100 meters, that's 56 kJ of energy expended fighting drag. In contrast, Bolt's peak kinetic energy (0.5*200 kg*(10.4 m/s)2) is 10.8 kJ. Not quite the 92% margin given by the study, but then again I didn't factor in form drag, so....

about maximizing the time spent with your feet on the ground; I think this is actually the opposite of what sprinters do. All sprinters who have set records toe strike, which minimizes the time their feet spend in contact with the ground. They're landing and immediately bursting off that foot. Number of strides between most sprinters is roughly equal; stride length is the biggest difference you see among sprinters.

Yeah, I didn't phrase that quite right. I meant that the force exerted on the ground as a function of time needed to be maximized. You're correct that this means foot-on-ground time is minimized.

Schrollini wrote:
davidstarlingm wrote:Well, the work done should fall off significantly with velocity, but force should be roughly constant.

I don't buy that.
  1. Try running on gravel. As you accelerate, you'll toss pieces of gravel backwards, but once you're up to speed, you won't. This means the horizontal force you're exerting on the gravel surface must be less than that during acceleration.

I'm thinking the number of gravel pieces tossed isn't a direct indicator of force. The faster you're moving, the less time you're in contact with any one piece of gravel, and so the less chance you'll have to kick pieces up.

Try running on wet grass, compared to dry grass. You'll accelerate more slowly, since the coefficient of friction is lower and the force you can exert before slipping is lower. But you can still reach the same top speed, so the force exerted at top speed must be less than that during acceleration.

Sure, with a lower-friction surface, this will change. But the track (and Bolt's shoes) are specifically designed to provide the absolute highest possible friction. So slippage will be negligible.

By their calculation, the drag force Bolt feels is about equal to his weight. Assuming that the center of drag and center of mass are in about the same place, this means he must be bent forward at 45o for torque balance around his feet. But he and all sprinters stand nearly upright during the cruise section of the race.

I just went and watched a video of Bolt running the 100-meter.

Man, he's fast.

But you're right, he doesn't seem particularly hunched over, except on launch. His acceleration is nearly at 45 degrees, but he's almost entirely upright by the time he finishes.

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Wed Jul 31, 2013 4:29 pm UTC

davidstarlingm wrote:This is a very rough estimate, of course, but 126 lbs is 560.5 N. Over 100 meters, that's 56 kJ of energy expended fighting drag. In contrast, Bolt's peak kinetic energy (0.5*200 kg*(10.4 m/s)2) is 10.8 kJ. Not quite the 92% margin given by the study, but then again I didn't factor in form drag, so....
Well, headsplode.
davidstarlingm wrote:Man, he's fast.

But you're right, he doesn't seem particularly hunched over, except on launch. His acceleration is nearly at 45 degrees, but he's almost entirely upright by the time he finishes.
The really amazing thing about his WR setting race was that he stopped sprinting like 10 yards from the finish and just sort of cruised on through.

But about his 'hunched' profile; sprinters balance their starts by not lifting their heads until they reach near max speed. This allows them to remain leaning forward and accelerate faster (and probably incidentally maintain a lower drag profile), but they are capable of their longest strides if they're standing as tall as possible.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
davidstarlingm
Posts: 1255
Joined: Mon Jun 01, 2009 4:33 am UTC

Re: Runner on a Treadmill

Postby davidstarlingm » Wed Jul 31, 2013 6:14 pm UTC

Izawwlgood wrote:About his 'hunched' profile; sprinters balance their starts by not lifting their heads until they reach near max speed. This allows them to remain leaning forward and accelerate faster (and probably incidentally maintain a lower drag profile), but they are capable of their longest strides if they're standing as tall as possible.

Hmm. So might increasing stride length allow for progressively better balance, making the leveraging of air resistance less important?

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Wed Jul 31, 2013 6:45 pm UTC

davidstarlingm wrote:
Izawwlgood wrote:About his 'hunched' profile; sprinters balance their starts by not lifting their heads until they reach near max speed. This allows them to remain leaning forward and accelerate faster (and probably incidentally maintain a lower drag profile), but they are capable of their longest strides if they're standing as tall as possible.

Hmm. So might increasing stride length allow for progressively better balance, making the leveraging of air resistance less important?
Not sure; Bolt finished the 100m in 41 strides, while the average was 44-6 (that's really remarkable to me, that it's such a tight range), which suggests he spent more time in the air, and thus more time fighting air resistance. I don't know how stride length correlates to balance, but I would imagine that shorter strides = more strides = better balance, since you have more opportunities to correct imbalances. But that's again, just a gut impression.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

User avatar
Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.

Re: Runner on a Treadmill

Postby Tass » Wed Jul 31, 2013 7:04 pm UTC

Izawwlgood wrote:
davidstarlingm wrote:
Izawwlgood wrote:About his 'hunched' profile; sprinters balance their starts by not lifting their heads until they reach near max speed. This allows them to remain leaning forward and accelerate faster (and probably incidentally maintain a lower drag profile), but they are capable of their longest strides if they're standing as tall as possible.

Hmm. So might increasing stride length allow for progressively better balance, making the leveraging of air resistance less important?
Not sure; Bolt finished the 100m in 41 strides, while the average was 44-6 (that's really remarkable to me, that it's such a tight range), which suggests he spent more time in the air, and thus more time fighting air resistance. I don't know how stride length correlates to balance, but I would imagine that shorter strides = more strides = better balance, since you have more opportunities to correct imbalances. But that's again, just a gut impression.


Air resistance does not disappear just because one touches the ground.

Also you don't know if it is his air time or his ground time that is longer. Longer legs could plausibly lead to longer distance in contact with the ground.

User avatar
Izawwlgood
WINNING
Posts: 18686
Joined: Mon Nov 19, 2007 3:55 pm UTC
Location: There may be lovelier lovelies...

Re: Runner on a Treadmill

Postby Izawwlgood » Wed Jul 31, 2013 7:08 pm UTC

Tass wrote:
Izawwlgood wrote:
davidstarlingm wrote:
Izawwlgood wrote:About his 'hunched' profile; sprinters balance their starts by not lifting their heads until they reach near max speed. This allows them to remain leaning forward and accelerate faster (and probably incidentally maintain a lower drag profile), but they are capable of their longest strides if they're standing as tall as possible.

Hmm. So might increasing stride length allow for progressively better balance, making the leveraging of air resistance less important?
Not sure; Bolt finished the 100m in 41 strides, while the average was 44-6 (that's really remarkable to me, that it's such a tight range), which suggests he spent more time in the air, and thus more time fighting air resistance. I don't know how stride length correlates to balance, but I would imagine that shorter strides = more strides = better balance, since you have more opportunities to correct imbalances. But that's again, just a gut impression.


Air resistance does not disappear just because one touches the ground.

Also you don't know if it is his air time or his ground time that is longer. Longer legs could plausibly lead to longer distance in contact with the ground.
Hmm. I was basing this assumption of the fact that he takes fewer strides than the average runner, but has the same stride rate. While it's possible that he extends the 'foot in contact with ground' portion of his stride, it seems unlikely to me that any individual part of his stride is different (the 'push off with your foot' portion just contains more oomph than anyone else)

Those assumptions aside though; sprinting is not speed walking; it's effectively leaping from one foot to the other. The more time you spend with your feet on the ground, the more time you're spending not leaping to the next foot.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

Carnildo
Posts: 2023
Joined: Fri Jul 18, 2008 8:43 am UTC

Re: Runner on a Treadmill

Postby Carnildo » Thu Aug 01, 2013 6:23 am UTC

idobox wrote:What other sources of energy loss are there?
Friction with ground and inelastic deformation are the only ones I could come up with. I have no idea how much power we can loose by deforming our bones and tendons inelastically, but I assume it's rather small. With good shoes, you shouldn't drift much. There is of course deformation of the shoes and track left.

The number I've heard for this is that a good runner will lose about 10% of their energy to deformation (not only bones and tendons, but also muscles, shoes, track, and everything else) with each stride. The big controversy about the runner with two artificial legs was that the springs in them gave him less than 5% loss, which could be considered an unfair advantage.

Schrollini wrote:By their calculation, the drag force Bolt feels is about equal to his weight. Assuming that the center of drag and center of mass are in about the same place, this means he must be bent forward at 45o for torque balance around his feet. But he and all sprinters stand nearly upright during the cruise section of the race.

The 45-degree angle is only true for static balance. When looking a sprinter, you need to model things dynamically, so you can (for example) balance drag against inertia rather than gravity.

User avatar
eSOANEM
:D
Posts: 3652
Joined: Sun Apr 12, 2009 9:39 pm UTC
Location: Grantabrycge

Re: Runner on a Treadmill

Postby eSOANEM » Thu Aug 01, 2013 9:53 am UTC

Carnildo wrote:
Schrollini wrote:By their calculation, the drag force Bolt feels is about equal to his weight. Assuming that the center of drag and center of mass are in about the same place, this means he must be bent forward at 45o for torque balance around his feet. But he and all sprinters stand nearly upright during the cruise section of the race.

The 45-degree angle is only true for static balance. When looking a sprinter, you need to model things dynamically, so you can (for example) balance drag against inertia rather than gravity.


That's not how dynamics works.

If the sprinters running at a constant speed, there are no inertial forces and, if the drag is equal to their weight, they must be inclined at 45o or topple. If they're accelerating, the inertial force acts backwards meaning they will need to lean even further forwards. If on the other hand they're decelerating, then and only then can you balance some of the drag with an inertial force.

Note, all of this depends on acceleration because physics doesn't care how fast you're moving (due to the equivalence of inertial frames), only how quickly that changes.
my pronouns are they

Magnanimous wrote:(fuck the macrons)

User avatar
Copper Bezel
Posts: 2426
Joined: Wed Oct 12, 2011 6:35 am UTC
Location: Web exclusive!

Re: Runner on a Treadmill

Postby Copper Bezel » Thu Aug 01, 2013 11:15 am UTC

If the sprinters running at a constant speed, there are no inertial forces and, if the drag is equal to their weight, they must be inclined at 45° or topple.

Doesn't this mean you're assuming that the runner's feet act to apply torque to one end of the runner? If the force is applied radially from the center of gravity, there's no torque at all, right? A runner's stride is applying force downward to lift off the ground and backward to combat drag. If those forces are equal, then you just need a force whose vector is through the center of gravity that's at a 45° angle, right? Don't runners' legs generally end up a bit behind their torsos while pushing off? = )
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

she / her / her

User avatar
eSOANEM
:D
Posts: 3652
Joined: Sun Apr 12, 2009 9:39 pm UTC
Location: Grantabrycge

Re: Runner on a Treadmill

Postby eSOANEM » Thu Aug 01, 2013 1:23 pm UTC

If the runner is in equilibrium (i.e. not toppling), then it doesn't matter where we take moments about.

If we take moments about the runner's feet there's no moment from that force and we only need to consider their weight and the drag.
my pronouns are they

Magnanimous wrote:(fuck the macrons)

User avatar
Schrollini
Posts: 515
Joined: Sat Sep 29, 2012 5:20 pm UTC

Re: Runner on a Treadmill

Postby Schrollini » Thu Aug 01, 2013 1:28 pm UTC

Copper Bezel wrote:
If the sprinters running at a constant speed, there are no inertial forces and, if the drag is equal to their weight, they must be inclined at 45° or topple.

Doesn't this mean you're assuming that the runner's feet act to apply torque to one end of the runner?

I was doing the torque balance around the runners feet. Since the forces applied by the feet have no lever arm, they result in no torque. The only torques are from gravity, acting on the center of mass, and drag, acting on the center of drag. These forces are acting at right angles to each other. If they are equal in magnitude, as this paper claims, and the centers of mass and drag are co-located, which seems more-or-less reasonable, they must be inclined at 45° to balance the lever arms of these torques.

Or, what eSOANEM said.

Copper Bezel wrote:Don't runners' legs generally end up a bit behind their torsos while pushing off? = )

Absolutely. But they are accelerating then, so you can't use static force balance.
For your convenience: a LaTeX to BBCode converter

User avatar
davidstarlingm
Posts: 1255
Joined: Mon Jun 01, 2009 4:33 am UTC

Re: Runner on a Treadmill

Postby davidstarlingm » Thu Aug 01, 2013 1:31 pm UTC

Copper Bezel wrote:
If the sprinters running at a constant speed, there are no inertial forces and, if the drag is equal to their weight, they must be inclined at 45° or topple.

Doesn't this mean you're assuming that the runner's feet act to apply torque to one end of the runner? If the force is applied radially from the center of gravity, there's no torque at all, right? A runner's stride is applying force downward to lift off the ground and backward to combat drag. If those forces are equal, then you just need a force whose vector is through the center of gravity that's at a 45° angle, right? Don't runners' legs generally end up a bit behind their torsos while pushing off? = )

Yeah, I'm thinking that things like torque are probably accounted for by the path taken by a person's legs. When I'm running, my leg is around a 45o angle at the termination of my push-off, so perhaps that's how the force vector gets adjusted for (particularly if the extension of my other leg balances out the torque on my waist).


Return to “Science”

Who is online

Users browsing this forum: No registered users and 8 guests