A question about the gym

[Fulk]

Can anybody help with the following?

My wife and I have just started going to the gym . . .which is pretty boring but it does seem to be having some benefits.

Anyway, there's a step machine that rotates towards you and you step up, just as if you were trying to go up a down escalator. The height gained is given in 'storeys' – so I counted the number of steps it took to make one storey and then measured the height of the steps to work out that one storey is equivalent to 10 feet. So typically if I go on this machine I'll do 60 storeys, or a putative 600 feet. But it sure doesn't feel like 600 feet, it feels a fair bit less. For example the other day we walked up Ingleborough from the Hill Inn, which route contains a very steep section that climbs ~70 m (~230 feet) in a horizontal distance of ~100 m and it felt like much harder work than climbing the greater distance in the gym. Similarly on the treadmill the other day I did a putative 2 km at a gradient of 15%, so I suppose this means that I climbed 300 m or ~1000 feet; again it didn't feel like that.

So – the question is, 'Is the supposed height and distance covered a realistic representation, or is it actually less on account of the machine doing some of the work?'.

(Incidentally, a similar question could be raised about the prusik race at Hidden Earth.)

 

[alanw]

Steve Mould has a video on this subject

 

[Fulk]

Thanks for that, alanw.

 

[Pitlamp]

That steep path up from the back of the Meregill catchment is very uneven underfoot. It'll make you use extra stabilising muscles as well as your quads and calves to raise your body weight. That - and the fact that no two steps are the same height on that steep path - will make it feel a bigger / harder climb than it actually is, I suspect. In the gym you don't need to concentrate on every foot placement, allowing your mind to wander.

 

[TheBitterEnd]

I've seen that Steve Mould video before and I think his method may be flawed because wheels are not the same as legs. I am inclined (pun) to think that on a stepper or inclined tread mill when walking or running you lift your leg and step up but at the same time the elevation of your foot is moving down so by the time you have completed your "step up" your foot has returned to the elevation at which it started. If it didn't you would run off the end of the machine. When climbing a real hill you have to fully lift your body weight by the height of the step but on the treadmill you start lifting your body weight but as your foot moves downwards you are straightening your leg without lifting your body. My first and probably naive guess is that the tread mill is probably around 50% of the power requirement.

 

[Chocolate fireguard]

If your actions on the treadmill are the same as they would be on a smooth slope of the same gradient the energy is the same.
On a real hill it may be different, as has been pointed out.

 

[Fulk]

My gut instinct is to go with TheBitterEnd here. I guess I'll just have to go and find a 600-ft tower block or sky-scraper and see how long it takes me to climb 600 feet and how knackered I feel after doing so!!!

 

[Chocolate fireguard]

It's just about what happens to your Centre of Mass.
When you step up on the treadmill you bring your C of M back up the same distance that the treadmill has lowered it.
On the slope the same step lifts your C of M the same distance.

 

[Pitlamp]

My gut instinct is to go with TheBitterEnd here. I guess I'll just have to go and find a 600-ft tower block or sky-scraper and see how long it takes me to climb 600 feet and how knackered I feel after doing so!!!

There's a video on You Tube of a bloke who lives in Cambridge. He wanted to run the Bob Graham Round in the Lake District, self supported. Cambridge isn't exactly hilly and the only way he was able to train was to run up and down stairs in a multi story car park, incessantly.

For anyone unfamiliar the Bob is a run around the Lake District of something like 65 miles, involving 42 mountains, which needs to be completed within 24 hours. The Cambridge fella succeeded, which I reckon was a damn fine effort.

 

[andybrooks]

I've seen that Steve Mould video before and I think his method may be flawed because wheels are not the same as legs.

I think that what might be missed by the Galilean relativity model and by Steve Mould’s experiment is that the speed of the machine is likely to be variable. The human body places a load on the device which is likely a significant fraction of its maximum, and the machine’s response will not be instantaneous. I suspect that the steps will accelerate downward at the start of each step (when the body is working hardest on bent knee), and the corresponding upward acceleration will take place on a straighter knee which can absorb it with less effort.

 

[pwhole]

A few years ago I worked on a rope-access job painting a brand-new multi-storey car park lift shaft in Liverpool. The lifts weren't yet installed, and so we had to climb fifteen floors up the stairs, at least four times a day, for five weeks, carrying large buckets of very heavy mineral paint up with us. By week three we could get to the top without stopping for a breather, but it never got 'easy'. The paint was fantastic though! (Keim)

I would have liked to claim that I was much fitter by the end, but unfortunately my appendix burst in the hotel on the final night, and I ended up stuck in Liverpool hospital for another week - and then the inevitable recuperation period meant that any benefits I'd accrued from all the exercise were lost. Though the doctor said I recovered a lot quicker than most, so maybe it did help a bit

 

[TheBitterEnd]

If your actions on the treadmill are the same as they would be on a smooth slope of the same gradient the energy is the same.
On a real hill it may be different, as has been pointed out.

A real slope is not moving down hill as you move up, unless it's a scree slope.

The other thing that Mould doesn't consider is the potential energy at the end of the run. If the car ran off the top of the ramp and landed on your foot it would hurt more than if that happened with the one on the treadmill. The car running up the ramp has more potential energy than the one on the treadmill when it stops. That potential energy must have come from somewhere.

 

[Chocolate fireguard]

I think that what might be missed by the Galilean relativity model and by Steve Mould’s experiment is that the speed of the machine is likely to be variable. The human body places a load on the device which is likely a significant fraction of its maximum, and the machine’s response will not be instantaneous. I suspect that the steps will accelerate downward at the start of each step (when the body is working hardest on bent knee), and the corresponding upward acceleration will take place on a straighter knee which can absorb it with less effort.

It doesn't matter whether the speed of the treadmill is constant, variable between steps or variable within the step, during the step duration it will have tried to lower you vertically by a certain amount, which will depend on the treadmill speed, but the energy you have expended staying in the same place will be the same as that you would expend gaining that same vertical height on a smooth slope with the same walking/running style.

In the case of the machine Fulk described the vertical height per step is fixed.

Fulk also asked about the prusik race at Hidden Earth. I don't do HE, but I assume the rope is lowered as someone climbs it?
There was a thread on here some time ago (a year, less?) about the design of such a system for training.

 

[ChrisB]

Fulk also asked about the prusik race at Hidden Earth. I don't do HE, but I assume the rope is lowered as someone climbs it?

Yes. It's a parallel situation and provides me with another way of thinking about it.

When you prusik up a pitch, you gain potential energy (mgh). When you abseil that pitch, you lose exactly the same amount, and it turns into heat in your descender. So if somebody lowers a rope, with your weight on it, with the same length of rope running through a descender, that dissipates the same energy as abseiling the pitch, which is the same energy as climbing the pitch, and also (because the energy must balance) the same energy you expended climbing the moving rope.

In the real prusik race there's energy lost in the pulley at the top but the pulley is frictionless in the thought experiment.

 

[Cantclimbtom]

A few years ago I worked on a rope-access job painting a brand-new multi-storey car park lift shaft in Liverpool. The lifts weren't yet installed, and so we had to climb fifteen floors up the stairs, at least four times a day, for five weeks, carrying large buckets of very heavy mineral paint up with us. By week three we could get to the top without stopping for a breather, but it never got 'easy'. The paint was fantastic though! (Keim)

I would have liked to claim that I was much fitter by the end, but unfortunately my appendix burst in the hotel on the final night, and I ended up stuck in Liverpool hospital for another week - and then the inevitable recuperation period meant that any benefits I'd accrued from all the exercise were lost. Though the doctor said I recovered a lot quicker than most, so maybe it did help a bit

But think how even better all your fitness would've been (without the appendix issue) if they'd insisted you all jugged up the ropes and walked back down the stairs for 5 weeks. Maybe next job???

 

[Steve Clark]

The actual energy that goes into the ‘mgh’ element of prussicking is pretty small. Say you climb a 30m pitch in 5mins. That’s 80x10x30=24,000J over 5x60=360s =66watts.
33 watts if it takes (me) 10mins.

A human sat at a desk just breathing is about 80w. Amateur cyclist can do 200w for an hour no bother.

There’s presumably a lot more energy lost to extra movements of the CoG, relax phase, stability muscles etc.

 

[pwhole]

But think how even better all your fitness would've been (without the appendix issue) if they'd insisted you all jugged up the ropes and walked back down the stairs for 5 weeks. Maybe next job???

To be honest, if we were below five or six floors, I did sometimes climb up the rope, as it was still less energy than climbing all the way to the top and abseiling back down. I tied the bucket to the end of the rope and just hauled it up on a jammer and pulley.

 

[mikem]

The main problem with the prussik analogy is that when you are higher up there is more weight of rope, so it slides through jammers better, whereas when you are lower, you end up lifting the rope below every time you move up

 

[TheBitterEnd]

Pondering the car on a ramp vs inclined treadmill some more ...
Assume a theoretical car has no bearing friction or rolling resistance then the car needs no energy input to stay in place on the treadmill (it needs a force to stop it rolling down). To push the same car up the ramp does need energy,
W=F d cosθ = m g d cosθ

 

[ChrisB]

Assume a theoretical car has no bearing friction or rolling resistance then the car needs no energy input to stay in place on the treadmill

That's true. But on the other hand, the friction force between the tyres and the treadmill is the same as between the tyres and the ramp. So the torque required from the engine is the same, and the rpm is the same, so the energy expended by the car is the same.

But on the treadmill, that energy doesn't become gravitational potential energy - so where does it go? Is it the energy required to control (brake) the treadmill?