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Treadmill question - don't worry there's no plane

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 john arran 26 Nov 2014
Having the misfortune to have to use a treadmill lately for exercise and sanity I've become curious about the physics of it. Specifically what causes it to be harder when you set the machine at a higher speed.

Effectively all you're doing at any speed is running on the spot, so clearly you're not doing any more work in a basic Newtonian sense.

When you're running on the road you need to accelerate on each stride to compensate for the deceleration that naturally occurs while you're in the air, but on a treadmill there's no deceleration because there's no velocity to start with.

Is it a vector force issue, in that to propel yourself 10cm upwards you also need to propel yourself horizontally too with respect to the moving surface? And if so, is it this which provides the main difficulty running on the road too, rather than friction or air resistance?
 ClimberEd 26 Nov 2014
In reply to john arran:

On a different (but related) note, lots of runners use it on 1% to provide a little more resistance and make it more akin to running on the road (effort/speed). This will also give some deceleration (although rather small.)

Harder at higher speed will be faster muscle contractions required.
 Andy Hardy 26 Nov 2014
In reply to john arran:

If you stood on a treadmill, you'd fall off the back, so you're constantly leaping forward, although your point of take off is moving backwards. Net result is you don't move relative to the ground.
 Marek 26 Nov 2014
In reply to john arran:

The analysis would be quite complex, but the two main 'sinks' for the energy you are expending will probably be the up-and-down bouncing of most of your body weight plus the cyclic acceleration/deceleration of your legs (and arms to a lesser extent). As you go faster the up-and-down movement increases a bit (frequency or height depending on your stride), but most of the increase will be in the 'amplitude' and frequency of the leg movements. I suspect (but can't prove) that that is where most of you energy increase goes (assuming flattish slope). An interesting question then is why when you put the treadmill on a slope it becomes harder. You are not actually lifting you body weight more (as you would on a real world hill). An exercise for the student...
OP john arran 26 Nov 2014
In reply to 999thAndy:

> If you stood on a treadmill, you'd fall off the back, so you're constantly leaping forward, although your point of take off is moving backwards. Net result is you don't move relative to the ground.

True, because when you're walking the treadmill surface is constantly propelling you backwards. But when running you're only in contact with this force for part of the time, so you might expect running to be relatively easier than walking - but it isn't.
In reply to john arran:

But what about if the treadmill is on a aeroplane?
 hamsforlegs 26 Nov 2014
In reply to john arran:

Non sciencey speculation ahead. Hopefully someone with actual knowledge will be along soon.

I've always guessed that you're about right if you assume a moderate pace on a flat, straight track. ie it's just the work required to accelerate along the belt while 'jumping'. This needs to include enough forward propulsion that you can also swing through with the trailing leg without ending up moving backward. I always found the 1% trick felt 'right' as it seemed to get the need for propulsion to match the kind of effort I was used to at a given stride length and cadence.

I think there are lots of additional factors when you run normally. Air resistance probably is quite significant as you run more quickly, and is potentially quite a major factor when you're really shifting. In the real world, though, you also do a fair bit of accelerating; up and down off pavements, over bumps, changing direction, looking around etc. I suspect these factors are actually quite a drain. Since on a treadmill you're not actually accelerating your physical mass, these effects are completely eliminated, which for me means that treadmills are a grind that hits my upper legs and lungs while real running seems to vary more over a session and is hard on my lower legs and core.

I did some testing a few years back on a Woodway motorless curved treadmill. They're designed for performance training, and have a curve and some kind of damping that gives natural resistance and control. The gradients seem to give the a natural feeling 'effort curve' across the stride. This seemed to give a much better emulation of the kind of stresses associated with running, including a more natural sense of regulating/changing pace. More than that, you can feel a progressive sense of having to pull through and then push off; it's this transition and sense of moving a mass that is missing for me on a normal treadmill.
 Mike Stretford 26 Nov 2014
In reply to john arran:

> True, because when you're walking the treadmill surface is constantly propelling you backwards. But when running you're only in contact with this force for part of the time, so you might expect running to be relatively easier than walking - but it isn't.

When the treadmill is at run speed you have to work harder to keep yourself on the treadmill while your foot is in contact, you run (leave contact with the treadmill part of the time) to make this easier but it is still harder than walking.
 hamsforlegs 26 Nov 2014
In reply to Marek:

I think you probably are having to accelerate your body mass upward much more when you put the mill on a gradient (or rather, you are having to provide a larger portion of the necessary resistance to acceleration under gravity). Put a treadmill on a very steep gradient and this is obvious; in fact, at a low cadence you even begin to oscillate and have to climb out of the hole on each stride.
 The New NickB 26 Nov 2014
In reply to john arran:

There is a greater force pushing you backwards, you counteract that force by minimising fiction and applying a force in the opposite direction, the faster the treadmill, the great the force and the greater the effort to counteract it. Remember that every time your foot hits the treadmill, there is a force acting on your body.

Or have I misunderstood the question?
 Mike Stretford 26 Nov 2014
In reply to john arran:

> Having the misfortune to have to use a treadmill lately for exercise and sanity I've become curious about the physics of it. Specifically what causes it to be harder when you set the machine at a higher speed.

> Effectively all you're doing at any speed is running on the spot, so clearly you're not doing any more work in a basic Newtonian sense.

> When you're running on the road you need to accelerate on each stride to compensate for the deceleration that naturally occurs while you're in the air, but on a treadmill there's no deceleration because there's no velocity to start with.

I think you've got this bit wrong. We can only beat gravity for so long.... each step of our run is about absorbing the energy of our 'fall' without tripping over, then propelling ourselves up and forward again. I assume horizontal deceleration while airborne is negligible.
OP john arran 26 Nov 2014
In reply to Mike Stretford:

> When the treadmill is at run speed you have to work harder to keep yourself on the treadmill while your foot is in contact, you run (leave contact with the treadmill part of the time) to make this easier but it is still harder than walking.

If I'm understanding you correctly, by your reasoning the difference in effort between jogging and walking at 6kph on a treadmill would be less than the same difference on a road - i.e. even though jogging would still be harder than walking it wouldn't be as much harder as it would on the road. Unfortunately this doesn't seem to be the case, as at every speed the perceived effort of walking, jogging or running on a treadmill is very close to what you would expect on a road. For that reason I don't think the effort expended can have anything to do with the proportion of foot contact time.
OP john arran 26 Nov 2014
In reply to Mike Stretford:

> I think you've got this bit wrong. We can only beat gravity for so long.... each step of our run is about absorbing the energy of our 'fall' without tripping over, then propelling ourselves up and forward again. I assume horizontal deceleration while airborne is negligible.

Not sure which bit you're saying I have wrong as I was only talking about horizontal velocity and acceleration - or lack of. Assuming we gain the same height while running as while jogging on the spot, that only leaves the horizontal component to consider.
 Mike Stretford 26 Nov 2014
In reply to john arran:
> If I'm understanding you correctly, by your reasoning the difference in effort between jogging and walking at 6kph on a treadmill would be less than the same difference on a road - i.e. even though jogging would still be harder than walking it wouldn't be as much harder as it would on the road. Unfortunately this doesn't seem to be the case, as at every speed the perceived effort of walking, jogging or running on a treadmill is very close to what you would expect on a road. For that reason I don't think the effort expended can have anything to do with the proportion of foot contact time.

No that isn't what I meant.... to be fair I did conflate 2 aspects of the question.

1) To stay in the same place relative to the room, you have to move at a certain velocity relative to the treadmill surface, you achieve this by traction.....same as you would on the road. As on the road you also have to work at decelerating and accelerating vertically.

2) You adopt a run because your body cannot provide the necessary traction walking.

EDIT: I've seen those fast walkers at the Games but they don't half look silly!
Post edited at 18:23
 Mike Stretford 26 Nov 2014
In reply to john arran:

> Not sure which bit you're saying I have wrong as I was only talking about horizontal velocity and acceleration - or lack of. Assuming we gain the same height while running as while jogging on the spot, that only leaves the horizontal component to consider.

Yeah but you did talk about how it 'feels'.Some of the work we 'feel' is the vertical aspect, so there would be no change there. I think the only difference in forces is actually air resistance and it is negligible at walking/running speed.

 deepsoup 26 Nov 2014
In reply to john arran:
> Effectively all you're doing at any speed is running on the spot, so clearly you're not doing any more work in a basic Newtonian sense.

In a basic Newtonian sense, running on the spot is *exactly the same* as running in a straight line at a constant velocity.
OP john arran 26 Nov 2014
In reply to deepsoup:

Well spotted, smadass. Now if you'd like to apply your acute mind to the original question ...

Actually your comment is perhaps more insightful than it first appears. Clearly, according to you and Newton anyway, any difficulty experienced in maintaining any running speed (beyond the difficulty of jogging on the spot anyway) will be that of preventing yourself from slowing down, so we must ask what is it that slows a runner down. Air resistance isn't a major factor so it must be friction due to contact with the ground, which seems odd to me since there's no contacting surfaces moving relative to one another - my usual conceptual idea of friction.

NickB said earlier that "every time your foot hits the treadmill, there is a force acting on your body", which is undoubtedly true but that's not so obviously the case on the road, where there is no clear agent of force. It seems in fact that friction, even in highly efficient athletes, provides quite a formidable opponent,

Why then is it that a runner cannot move across the ground with a similar amount of friction to a cyclist? Biomechanical energy wastage can't be that different, and the rubber contact areas are broadly comparable. Why the huge difference?
 henwardian 26 Nov 2014
In reply to john arran:

Unless you are sprinting or are running into a fair old breeze, the decelleration due to air resistance is negligable. You can see this if you cycle a bike up to about 10mph on the flat and then coast; it takes a long time to stop and even then, there is significant decelleration due to the tyres on the road surface. Force of the air on you increases with the square of the movement speed so while you might think "woah, this is some resistance" on sticking your head out of a car window at 50mph, a typical runner at 10mph is going to feel 25 times less resistance.

The angled treadmill is harder to run on because when you left your trailing leg, you have to lift it higher than you would if the surface where level because the back end of the treadmill is at a lower altitude than the front end. BUT, you are not gaining any altitude, as your foot travels from touching the ground back under you, it also falls in altitude, this means that you don't apply the force through that leg necessary to raise the rest of your body above the waist. So while running on a slanted treadmill is harder than running on the flat, it is easier than running up a real hill. (this assumes you precisely match treadmill speed at all times, if you run slightly faster then slightly slower by turns then you will be effectively gaining and then losing altitude with your trunk so it will feel a bit closer to a genuine uphill run).

Loads of things will make running outside more energy intensive, including:
lumps and bumps in land surface, kerbs, etc.
muscle response to keep you on track when your foot lands on uneven ground.
correction against wind buffeting from the sides.
extra effort if there is a strong headwind.
Energy to heat your body if you are running on a particularly cold day.

As you increase your speed on the treadmill, your grounded foot is travelling back faster so you have less time to bring the other foot forward for the next stride. If you want to stay above the treadmill (and not end up implanted in the wall behind you!), you have two options:
1) Stay in the air longer to give yourself more time for your trailing leg to make the passage through the air to being in front of you again.
2) Move your trailing leg through the air at a higher velocity so it goes from behind you to in front of you in less time.
For 1), aside from cheating, the only way to stay in the air longer is to bounce higher from every stride, this means more upwards acceleration which in turn means more energy to the muscles that contract and expand to propel you upwards against gravity.
For 2), If you bring your trailing leg forward at a higher velocity, your muscles have to use extra energy to accelerate the leg forwards just after you lift it up off the ground and extra energy to decellerate the leg to stationary (relative to you) just before it hits the ground again.

On a personal note. Running sucks!
Seriously, it is incredibly inefficient. I challenge anyone to spend 4 minutes gently freewheeling down a slight slope in the countryside and then honestly tell me that they preferred their experience running down it!
 henwardian 26 Nov 2014
In reply to john arran:
Why the huge difference?

The wheel.

A freewheeling cyclist only suffers decelleration from rubber to road friction, headwind friction and some minor crap like moving muscles to balance and ball bearing rubbing in the wheel hub.

The jogger has to constantly accelerate their body upwards (it is falling down by gravity every time that neither foot is on the ground) and constantly accelerate their arms and legs forward and backward.
It's hideously inefficient.
 Robert Durran 26 Nov 2014
In reply to john arran:

> Effectively all you're doing at any speed is running on the spot, so clearly you're not doing any more work in a basic Newtonian sense.

If you think that, then presumably you also think that you are effectively running at 500mph if you jog down the aisle of an aeroplane. This is clearly bollocks. All that matters in terms of effort is your speed relative to the treadmill/aeroplane/surface of the earth.
 Robert Durran 26 Nov 2014
In reply to ClimberEd:

> On a different (but related) note, lots of runners use it on 1% to provide a little more resistance and make it more akin to running on the road (effort/speed).

If running on a treadmill feels easier, then it is either an illusion or because there is no wind resistance or because the lack of movement relative to surroundings somehow messes with your mind and makes you change your running style to be les efficient. Biomechanically, there need be no difference whatsoever; they are precisely equivalent from a physics point of view.
XXXX 26 Nov 2014
In reply to john arran:

You're at rest with respect to the ground. With respect to any given point on the belt you're going forwards.

Is it just me that thinks this is a stupidly obvious question?

 deepsoup 27 Nov 2014
In reply to john arran:
> Well spotted, smadass. Now if you'd like to apply your acute mind to the original question ...

I think that's been done already. But nobody seemed to have pointed out the glaringly obvious, so I thought maybe I should.

> Actually your comment is perhaps more insightful than it first appears. Clearly, according to you and Newton anyway, any difficulty experienced in maintaining any running speed (beyond the difficulty of jogging on the spot anyway) will be that of preventing yourself from slowing down

I may be a smadass, but you're still not getting it - simplistically, there *is* no difficulty in preventing yourself from slowing down. That's what the Newton thing is all about: F=ma - you don't *have* to apply any force to maintain a steady speed.

If you're riding a perfectly efficient bicycle, coasting along on the level, maintaining a constant speed requires zero effort, just like remaining still does if you're already not moving. Likewise, if you had a really long treadmill, running on it 'on the spot' would be exactly the same as turning it off and running along it with a following wind.

> Why then is it that a runner cannot move across the ground with a similar amount of friction to a cyclist? Biomechanical energy wastage can't be that different, and the rubber contact areas are broadly comparable. Why the huge difference?

Running at a constant speed is harder work than coasting on a bike for exactly the same reason that jumping up and down on the spot is harder work than standing still. Biomechanical energy wastage *can* be that different and it is. If energy wasn't being wasted, running wouldn't make you hot.
 deepsoup 27 Nov 2014
In reply to henwardian:
> The jogger has to constantly accelerate their body upwards (it is falling down by gravity every time that neither foot is on the ground) and constantly accelerate their arms and legs forward and backward.

> It's hideously inefficient.

It's hideously inefficient for us humans (among many other animals) because we use our muscles to throw our bodies up into the air, and then to absorb the shock as we land (dissipating the energy, which mostly ends up as heat in our bodies) before doing it all over again.

Kangaroos bounce using elastic tendons to store and release energy - amazingly efficient. (Tigger was wrong - he was never the one with legs made out of springs!) It's like the difference between me or you jumping up and down on the spot versus bouncing up and down on a trampoline.
OP john arran 27 Nov 2014
john arran - on 04:55 Thu
Thanks all

I feel like I've been a bit blond on this thread - especially with the Newtonian slip in the OP but also in not realising immediately that, in the absence of significant wind resistance, the only relevant factor is speed relative to the road/treadmill surface (thanks Robert for the aeroplane comment)

I also realise that I've been confounding two issues; that of relative difficulty re road/treadmill and that of running difficulty per se.

Regarding running difficulty I still don't feel entirely happy with some of the explanations above - especially those that focus largely on vertical movement as the cause of the effort. There are two reasons for this: One is that running quickly feels very much harder than running slowly, and much harder than jogging on the spot, even though the height gained can be very similar in each case. I'm prepared to believe though that it may be the cardio system that's providing much of the additional perceived effort as it gets close to its sustainable limits, meaning 10% more actual effort could well feel twice as hard.

The second reason is that walking seems to exhibit very similar effort profile and doesn't need to involve any up and down motion at all. Those silly-looking race-walkers have a very level profile but even at comfortable speeds they're still hopelessly inefficient compared to a bicycle. I guess the human body doesn't have a near-frictionless hub nor kangaroo-style ERS.

So it seems like biomechanical inefficiency (and not surface friction or vertical waste) is actually at the root of the problem after all, and the only reason we don't see the same in cycling is that the near-frictionless hubs provide most of the efficiency and so biomechanical issues will only apply to movement/acceleration beyond coasting speed rather than to all forward movement.

As a final comment, the idea of using a 1% gradient to harmonise effort between treadmill and road at the same speed simply doesn't work in the hotel gyms I've been having to use. They're so bloody hot that running at any speed at all becomes phenomenally hard after just a few km!
 The New NickB 27 Nov 2014
In reply to john arran:
> NickB said earlier that "every time your foot hits the treadmill, there is a force acting on your body", which is undoubtedly true but that's not so obviously the case on the road, where there is no clear agent of force. It seems in fact that friction, even in highly efficient athletes, provides quite a formidable opponent,

On a treadmill to counteract the backwards force of the treadmill you apply a force forward and stay stationary. On the road you apply a force forward and go forward.
Post edited at 07:28
 hamsforlegs 27 Nov 2014
In reply to john arran:

In relation to the general running point; your legs/arms are really heavy! Deepsoup has captured a lot of this. Moving them around in a stable way and accelerating a trailing leg forward exerts a huge backward/sideways/shake-it-all-about force on your body, so you need to
a) accelerate or 'push off' hard to counterbalance all that swinging about get forward and setup for the next stride
b) exert a lot of energy to resist various wobbles and rotational forces

Running is not at all like a frictionless glide at a constant speed; it's a constant cycle of acceleration and deceleration in lots of directions all at once.

One simple indicator of this is how much energy it takes to swing a leg forward. Go for a race-pace run for 1-2 hours and I can feel my hip flexors and lower abs getting very tired. This suggests to me that simply accelerating my trailing leg to 'overtake' my body is hugely energy intensive, and must also require an additional boost from my driving leg to maintain forward momentum. Once I have to do all of that without stumbling/weaving/crying/vomiting there is a lot going on in the inefficiencies department.

On a correctly calibrated running machine, I've always found the perceived effort at a given speed to be both lower and different in quality from that on a road, which I've always put down to a slight reduction in the stumbling/weaving/crying/vomiting effect? Running in a gym is always like going for a run on a windless, humid 30 degree day. Use a fan.
 deepsoup 27 Nov 2014
In reply to john arran:
> They're so bloody hot that running at any speed at all becomes phenomenally hard after just a few km!

That's funny. I was thinking that the lack of air resistance might make running on a treadmill a bit easier (like having a following wind) - it hadn't occurred to me it might actually make it harder on account of the lack of ventilation.

Physics-y theorising aside - if you're currently confined to exercising in hotel gyms, commiserations, that sounds really rubbish!
 Robert Durran 27 Nov 2014
In reply to john arran:

> Regarding running difficulty I still don't feel entirely happy with some of the explanations above - especially those that focus largely on vertical movement as the cause of the effort. There are two reasons for this: One is that running quickly feels very much harder than running slowly, and much harder than jogging on the spot, even though the height gained can be very similar in each case.

When running at any speed, your feet are stationary when planted on the ground (and your legs are progressively less stationary the higher you go up them). Once lifted off the ground they have to be accelerated to a speed greater than the speed you are running at to "overtake" your body before being planted on the ground again. This takes energy and the faster you are running the more energy it will take.
XXXX 27 Nov 2014

Energy is proportional to v squared. It's not a difficult concept that moving something of a certain mass at a high velocity is going to take a lot more energy than the same mass at a lower velocity.

Cycling, well that involves a bike which has wheels. If I take a round thing and push it down a hill it will go on forever. If I take a runner shaped thing and push it down the same hill, it will not. Running is less efficient for a whole host of other reasons. A cyclist has all their work transferred to the surface in exactly the direction required and their arms are still. A runner doesn't.

I'm genuinely baffled about how this topic is still running. (sorry)
Post edited at 17:34
OP john arran 27 Nov 2014
In reply to Robert Durran:

Yes I like that explanation and it fits with my doubt about the vertical movement being a key factor.


In reply to deepsoup:

I have a couple of small battery-powered fans I clip onto the machine to help provide some airflow but as the temperature is around 24degC they only help a little. I get to a point after about 5k when I know I'm running very comfortably and not that fast but I start literally dripping with sweat, breathing gets more laboured and the effort required to run even at a steady pace becomes unbearable. Or is it in fact just boredom

Oh to be back home next week and climbing again!
OP john arran 27 Nov 2014
In reply to XXXX:

Would it be more efficient then if I were to keep my arms still?

csambrook 27 Nov 2014
In reply to john arran:

> Would it be more efficient then if I were to keep my arms still?

Yes. Sprinters use their arms to generate power, long distance runners tend to keep their arms still and down.
Over longer distances the limiting factor can end up being how much stored energy you can access to fuel your muscles so relaxing your arms means more available for the legs. (It's all about regeneration of a chemical known as ATP which transfers energy to where it's needed).
csambrook 27 Nov 2014
> I get to a point after about 5k when I know I'm running very comfortably and not that fast but I start literally dripping with sweat, breathing gets more laboured and the effort required to run even at a steady pace becomes unbearable. Or is it in fact just boredom

Please be really careful running 5km and above on a treadmill. As you've spotted, it's not the same as a real run and in particular it's much more repetitive so can lead to RSI type problems. On a real run each footfall will be slightly different but on a treadmill they are all identical.

I'm never too sure about the heat problem on a treadmill. Getting rid of excess heat is a critical part of running and can limit performance so I suspect running at a higher temperature in training makes you a better runner. Certainly I know some people who wear extra clothes on training runs for that reason.

csambrook 27 Nov 2014
In reply to john arran:

It's not answering your question but people often miss the fact that energy used running is to a first approximation proportional to the distance covered rather than the time spent running. That feels counter intuitive to most people as clearly running faster feels harder, and indeed it is, but of course you get to the finish sooner too.
So when considering a treadmill, at a higher speed setting you are having to move your legs faster so more muscle power is needed. But if you consider the effort spent covering the same length of belt at different speeds you should find it's about the same.
 Banned User 77 03 Dec 2014
In reply to ClimberEd:

Yeah for runners running 7min mile or quicker add 0.5-1%.. otherwise not much point..

I think it can help for cadence.

You are propelling yourself horizontally on a treadmill..

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