UKC

I was reading Uphill Athlete https://uphillathlete.com/training-for-mountaineering/ for a bit of background information on uphill training. These guys have loads of really good information and seem to be one of the best places to go to if you’re looking for info to train for uphill shenanigans.

But, and this is more of an interesting science problem, there was a sentence or two in the link above that jumped out that as it sounds wrong and I wanted to check that I’m not missing something.

Quote:

“Bear in mind that with these stair machines the step moves down as you step up. This means that you really only lift your entire body weight about 1/2 of the height of the step. Thats how your body manages to stay in the same place as the stairs move under you.”

Surely the above can’t be right?

The effort required is proportional to work done, and the work done is your movement (f x d) relative to your frame of reference (in this case the stairmaster, or more specifically, the moving part of the stairmaster).

Put another way. if the stairs have a vertical component of say 0.2m/s down (the number doesn’t matter) then for you to have a vertical component relative to the room of 0m/s (i.e., not moving) is exactly the same as climbing a set of stairs at a rate of 0.2m/s.

The same is true for the horizontal component.

The only difference would be wind resistance (negligible) and any other technique difference due to handle usage and changes in climb rate as you try to avoid rolling off the end of the machine etc.

I’m getting jumbo jets on escalators vibes. 

I'd say they're right. The knackering bit is raising your body mass relative to the Earth, so if you raise your body half a step it's half as knackering.

It's got to be providing less resistance than you would experience in the outdoors or the stairmaster wouldn't move downwards under the pressure of your foot, if it provided a resistance equal to your weight it wouldn't go down you'd go up......

I think that's correct 🤔 

Mark

But your frame of reference is the stairs, not the earth.

Think of it this way, if you're walking to the snacks coach on a moving train, it's no easier or harder to move with or against the direction of the train. This is because the train is your frame of reference.

The principals are exactly the same with a vertical component on the stairmaster.

I get jumbo jet on escalator vibes too, but I'll bite.  You're quite correct, that obviously isn't right.

Work = force x distance.  The force is your bodyweight (plus whatever you're carrying), and the distance you move it is the same whether you're lifting your body up or pushing your foot down. Indeed lifting your body up and pushing your foot down are the exact same thing seen from two different relative view points.

Ay, sure to be distracting. An interesting change of tack.

jk

It begins!

It doesn't provide a fixed amount of resistance, that's a function of the speed it's moving at.  (And that ratio of speed to resistance is what you set when you adjust the machine.)

It requires less force to move it slowly than it does to move it fast - so step slowly and it provides less resistance than your bodyweight and you sink towards the floor, step quickly and it provides more and you 'go up'. 

On average it provides a resistance exactly equal to your bodyweight throughout your session and you stay at the same height - and you govern that yourself with the pace that you're stepping at.  A bit like a treadmill (with or without a jumbo jet on it): once the machine is set and running it's your control of your own pace that keeps you from falling off the back or running off the front.

Yes, but the step isn't fixed and so d is half (or whatever) of what you were expecting.

It's like running up a down escalator - the energy required to climb each step is less than if it were stationary (but there are more steps).

Or lowering the Earth relative to your body mass.  They say when Chuck Norris does press-ups he doesn't lift his body up, he pushes the Earth down!

I don't understand how you come to this conclusion.

There is a mental aspect to it tho'. When I walk on a stationary escalator my brain freaks out and I feel really unbalanced. It's a weird feeling.

But everything else being equal, the effort is exactly the same.

Try weighing your self on an escalator (actually maybe don't, or if you do, don't tell anyone I told you to) but if you did, your weight would be exactly the same, so the effort is the same.

What's this reference? Not following. Sounds fun tho' 

No it isn't - 'd' is the difference in height of your foot relative to the centre of mass of your body from bent leg to straight leg.  If your leg was a piston it would be the length of travel of the piston - makes no difference to the power of the engine whether it's a steam locomotive moving along a track or a stationary engine pumping water.

From the point of view of your body it's the same on the Stairmaster as on the hill - foot comes up, foot goes down.  From the point of view of the Earth it's zero (you gain no height).  I don't understand where this "d = half" thing is coming from.

On the hill the energy you expend is converted into potential energy associated with the height gain - which you can release by rolling down the other side of the hill.  On the machine the energy you expend makes the machine hot.  (Or if you're clever you could harness some of it to run a small fan to give you a little breeze and charge an iPad showing you pictures of nice mountain scenery.)

Ha ha, yeah right!  Because you're new here.  <insert 'rolling eyes' emoji here>

Ok, try this.  Imagine two broken Stairmasters.  In the first one the mechanism is a bit sticky so that the stair doesn't move until you have fully stepped up on it and you are stationary with your full weight at rest -and then it subsides fully so you can repeat the process on the other step.

In the other, the mechanism is properly broken, so that the step offers no resistance at all when you try to weight it.

Energetically, the first is essentially just like climbing a normal step, work done = potential energy gained, which is then lost as heat as it then subsides.  In the other, essentially no work is being done, barring the marginal frictional losses.

I'd say a working Stairmaster is between these two extremes.  

Yes.  Which is exactly the same as a Stairmaster that is working perfectly, except that your body bobs up and down more instead of losing height at the same time as you are working to gain that height.  The machine that is working normally just cuts out the intermediate bit and converts the work done into heat directly without much of it becoming potential energy gained first.

In the other you can't gain any height because the step won't bear any weight, so the work done merely consists of lifting your leg up and putting it down again. 

The working Stairmaster (and the 'sticky' one) simulate walking up a hill, with or without a pause after each step - this one perfectly simulates the experience of marching on the spot, because in both cases your weight is supported on your left leg as you lift and lower the right, which meets no resistance at all until you put that foot down and lift up the other one.

Edit to add:

Between the two extremes is a working stairmaster that you're not stepping on fast enough to fully unweight the foot you're not stepping with.  (So you're therefore not getting 'off the ground', same as on the broken machine that offers no resistance.) 

The resistance increases with the speed of movement, you need to adjust the machine or up the pace of your steps.  It's the equivalent of falling off the back of a treadmill because you set it to a speed faster than you can actually run.

The distance going from straight leg to bent leg is the same but that leg has to carry more or less weight on the Stairmaster depending on how much weight you transfer to the handrail.

In "full cheat mode" you can pretty much just lock your arms on the handrail and then just move your feet.

Even just stabilising yourself with the handrail saves a lot of energy that's normally used to keep you from falling on your side.

Practically speaking, it does feel a lot a lot easier to go up 50 floors on the Stairmaster than it would be to go up a 50 floors of a building, at a similar speed.

But they clearly get it wrong as to why. I don't see where they get this half distance thing from.

The first rule of planes on treadmills is you don't talk about planes on treadmills...

https://www.ukclimbing.com/forums/off_belay/friday_disagreement_-_brainteas...

https://www.ukclimbing.com/forums/off_belay/airplane_on_a_conveyor_belt_-_c...

It is counter intuitive, so allow me to try a completely different example to see if it makes more sense.

You'll have to humor me for a bit.

Imagine you have a vertical smooth pole with a wheeled remote control car that can run up and down it. For this example, it's in a vacuum and friction magically doesn't exist.

If the car is driving up the pole, once it's finished accelerating and travelling at a constant speed, it only has to exert enough force to support it's own weight since there are no other losses present. Provided it does that, in the absence of friction and air resistance, it will hold a constant velocity.

Now imagine that pole is moving down vertically at a constant velocity. In order for the car to not fall down accelerating at 1g due to gravity (remember, no friction) it would have to exert a force on the pole again, equal to it's own weight.

Now the example with a StairMaster is way more complicated, but the fundamentals are the same.

The fact that say "This means that you really only lift your entire body weight about 1/2 of the height of the step" indicates to me that this is really thought through - it's rather imprecise. If I was lifting my body weight half the height of the step then I'd quickly end up sinking into the floor as the stairmaster lowers.

In lowering the user, the stairmaster reduces your gravitational potential energy by the height of the step x your mass x g. You then have to gain that back using your muscles to end up where you started. If you only lifted yourself half way, you'd end...half way back up.

Ah ha, thanks.

What's the second rule?

Fair point, I'd forgotten there even was a handrail you could lean on.

Happy to take your word for that.  My only practical experience of a Stairmaster is briefly having a go on one about 20 odd years ago.

"The effort required is proportional to work done, and the work done is your movement (f x d) relative to your frame of reference (in this case the stairmaster, or more specifically, the moving part of the stairmaster)."

Surely the force required to push the stairmaster step down is less than that required to lift the rest of me up a real stair? So overall less work is done on the stairmaster, even if my feet have moved the same total distance

Pushing a step down (i.e, putting all your weight on your foot) is exactly the same as lift you up.

Every force has an equal and opposite reaction (Newton)

If you are imagining floppy steps that can't take your weight then the whole system isn't going to work and you'll fall off the end of the StairMaster.

If there’s no friction the car will be falling at 1g whether the pole is there or not! How could you even tell whether the pole was moving?

However, if I’ve understood it, you example is like the real world situation of a helicopter either statically hovering or steadily ascending.  When it’s hovering, it’s effectively accelerating at 1g upwards (opposing the external force of gravity), when it’s climbing it needs to do that, plus contribute extra energy in order to gain potential energy by being higher.  

Not sure how a car can dive up a vertical pole even if it wasn't smooth?

I suppose a rack and pinion system would work. 

You aren't taking into account the mass of the pole and the car. Any force accelerating the car up will also accelerate the pole down. 

It's key not to cheat, put in your correct weight and don't lean on bars at all, improve your balance. If the stairs rotate at 30m horizontal distance per minute, which is likely about 20m vertical height as they aren't at 90 degrees you still have some forward movement, then that's your training, stepping 5cm, 15cm, 30cm up each time is largely irrelevant as the frequency of stepping must match the distance of the stairs rotating, otherwise you'll be in a heap under it. 

I think they are the best training for going uphill ever, arguably better training than just doing hills for the sake of it as you don't have potentially joint damaging descents. (Yes i know working muscles in descent is beneficial too).

There's no hiding a lack of fitness on a gauntlet. 

Only unlike many steppers which are just pistons or springs, the stair master rotates. You don't push it down, it rotates and you descend unless you step up. If you don't push your body weight up to the next step you'd be on the ground in 1-2secs. 

Not having been to a gym for 20+ years is showing! I'll have to have a Google, I just assumed they were the piston type

Don't get distracted with how the car drives up the pole. Not important. (but if it helps, assume it can apply a force to the pole, with no losses).

Not quite. There is no frame of reference change here.

It would more more like a helicopter hovering with a vertical down wind of 1m/s vs a helicopter increasing altitude at 1m/s. Assuming no weird fluid dynamics the energy required would be the same.

https://corehandf.com/product/stairmaster-gauntlet-8g/

When I was younger I did a bit of stair running. When I got jelly legs I definitely starting pulling on the banisters.  

My only reservation is your muscles behave differently going downhill, and you really need to practice both, so I think it's better to use real stair and go up and down them. At least that's what this "Chase Mountains" guy on youtube said. Sounded convincing.

So does it basically acts like a rope over a pulley? It's the mass on the other end of the rope that determines the resistance, not your body weight. 

I think there's a point somewhere where a little assistance to finish a session is ok, however you do see some on stairmasters who are doubled over the bars, or think they are doing dips. 

Indeed, breaking the body weight in descent uses strength and energy, arguably harder than up, as if you step down you've gained energy during that 30cm step downward, up is always the same. However, i think too much descent on tired muscles puts more load on the joints. 

The stairs are on a loop, a 2m ish belt, if you stand on them they'll descend, how fast they fall away under you depends on what you set as your body weight and effort / speed level.

Think of them as walking up the down escalator.

Lots of simplifications, assume constant forces R & L whist my right foot is descending etc

Supposing my right foot is on a step applying force R that drops by h and my left floor is on a step applying force L that rises by h.

R+L=W (my weight) so that I don't go flying off into space or crash through the floor.

Work done by right leg on step is R x h

Work done by step on left leg is L x h

Work done by me is R x h - L x h

If you don't believe that last formula, this imagine pedalling at constant cadence whilst freewheeling and standing up on a bike. R+L = W and R=L as cadence doesn't speed up or slow down. Freewheeling is zero effort because R x h - L x h is zero (apart from a bit of effort against friction at bearing surfaces such as chain, freewheel and knees!).

Does the rising step apply any force (L) to the rising foot/leg or is the machine designed to stall if you leave any weight on the rising step?

You mention varying effort as well as speed. For fixed speed, varying effort would correspond to the support by the rising step that means I don't have to push down so much on falling step. 

I get how this is true for bicycle pedals, but a StairMaster doesn't worth this way. The StairMaster is no different to an escalator, only tinyer.

So when going up steps leading with your right foot you have

R = your weight

L = just dangling there not really doing much as you drag it's self weight onto the next step.

So your equation above simplifies down to:

Work done by me is R x h

then L x H

then R x H

and so on

It's not like an escalator at all as an escalator takes me somewhere for zero effort rather than an exercise machine that takes me nowhere despite any efforts.

as an aside stairs and exercise can be counter intuitive, apparently,this  referred to by Michael Mosely on R4 recently.

"But there are even more health benefits, according to researchers at the School of Medical and Health Sciences at Edith Cowan University in Australia. They made an interesting discovery. The lead researchers asked 30 older, obese women to take part in a 12-week exercise program. During the 12 weeks, one group went either up or downstairs at scheduled times so the researchers could look at the impact each stair taking direction had on metabolic markers of health. The subjects did their respective workouts twice per week, and the researchers added more stairs over time to increase the challenge.

The results?  Contrary to what you might think, the subjects experienced greater improvements in health markers when they walked down the stairs as opposed to climbing flights of stairs. As you might expect, their bone mineral density increased and their balance improved. Unless you hold on to the side rails, going up and down stairs requires balance skills. They also experienced a drop in resting heart rate and blood pressure. Also significant is the group who walked down flights of stairs enjoyed greater improvements in resting heart rate and blood pressure relative to those who climbed stairs. Maybe going downstairs is harder than it seems!  At the least, it offers unexpected health benefits."

The steps don't rise back up, they rotate around inside the machine. I know exactly what you mean, step machines with pistons, springs etc.. you can effectively just rock your weight from left to right, but never actually step your whole mass upwards. 

That's because when you step down you break your mass, plus the energy gained from acceleration. However if you want strong legs going up hill, you'll need to replicate lifting, not slowing your weight.

Note. His series on little wins really is great, science driven, external experts on each subject matter too. 

You step up the whole step, as far as the stair climber is concerned the stairs may as well be fixed, you exert the same as a whole step on a fixed stair. The "extra" energy due to the fact that you're not actually rising relative to the ground, is balanced in the motor/brakes. For simplicity imagine a motorless one that only has brakes, they'll get warm as you climb.

More to the point. Forget this nonsense and try one for a while.

They are way harder than most people imagine and Amy misconception it's some 80s throwback exercise suitable only for fat people will very rapidly be dispelled!

I looked at buying one as a long term investment, but apart from being £5k they need the head room above normal ceiling heights. I think they are brutal, but fantastic when it comes to replicating hill work. 

You do not talk about planes on treadmills

Yeah, not practical for homes.

I went to the gym 4 times this week, hoping to use the stair climber while there, but every time both were busy and people queue for them (actually they have 3 but 1 is permanently broken)

I don't know how a stairmaster works but the answer seems to me to lie in the following question:

If you were to put one foot onto the next step but transfer your weight only in proportion to the descent of the next step, such that no actual work is being done in elevating the centre of your body mass, would the increase in perceived effort compared to walking on the flat be purely down to the inefficiency of standing with legs partially bent?

Stairmaster is arguably a little unique, hence the 5k price tag. Think of going up the down escalator, if you don't physically lift your whole weight up to the next step you'll head down. They don't have left and right foot padels, just one 50-60cm full width step that moves downward and you must step upto the next. 

How about spiders on a floating treadmill??

https://bigthink.com/life/jumping-spider-harvard/#Echobox=1653542321

... in which case I think the effort required could most likely be considerably less than for actually climbing stairs.

Some time ago I conceived a method of doing pull-ups (and actually won an informal pull-up competition using it!) in which, instead of raising my centre of mass with each pull-up, I instead would curl up and rotate my torso such that when my arms were extended, my curled-up legs were raised to compensate, and vice-versa. It looks more like a rotating motion than an up-and-down one, but it allows you to go from arms straight to arms fully bent, without raising centre of mass at all. Pretty hard on your core, but crucially it strains your arms a lot less. Seems to me that you could achieve something similar on a stairmaster by gradually transitioning from one stair to another rather than by stepping 'up' per se, thereby doing no actual work in terms of raising body mass, albeit with increased strain elsewhere, such as by holding partially bent leg positions for longer during each step transition.

Really interesting insight 

Worth a try, but I'm not sure it would work, I feel like I've tried every brand of stepper imaginable when deprived of hill access, most are dire, but stairnaster if you avoid using the hand rail are merciless, it's like powering direct up real hills at 10-20m vertical/min, or you can do reps and so on. 

Now this has got me curious I’ll be hitting the gym tomorrow and will run some experiments.

Cunning. But wouldn't work for the Stairmaster. All your weight is on the steps and they move down at a steady speed (unlike the pull-up bar). Your weight is distributed between two steps but that doesn't matter because they both move down at the same speed. So work is done on the Stairmaster at the rate weight*verticalVelocity (and is turned into heat by the friction brake). That work is done by the decrease in potential energy as your centre of mass moves down. The only way to avoid falling off the bottom is for your legs to do (at least) the same amount of work to raise your centre of gravity back to where it was. Which is exactly the same work you would do walking uphill at the same vertical rate. If anyone thinks differently, I have some perpetual motion machines to sell you.

maybe think biomechanical effort rather than work done by the object. the accelerations required by the stepping movement maybe less?

A better analogy may be doing exercise in a steadily descending lift, or a descending aircraft once it's achieved uniform descent rate. Any jumps or work against gravity you do will feel identical to that on the ground because there is no different force exerted on you, simply the same constant gravitational force acting on an object that is otherwise stationary with respect to its frame of reference.

interesting. your analogy sounds good to me. stairmasters help you reduce overall biomechanical effort (by minimising peak accelerations?)

funny how a  similar thread on a physics forum had to be temporarily locked such was the conflict of opinion

https://www.physicsforums.com/threads/stairmaster-physics.951634/

think i'll go with the answer here; https://physics.stackexchange.com/questions/643382/stair-machine-vs-stairs-...

Most steppers don't have moving stairs, just left and right foot rests that lever against springs, pulleys system or pistons. The stair master brand is a little unique in that respect, but I can see why it gets heated. In some respects going up a real hill is easier, you can vary your gait, foot angle on grass or rock, the variety of stepping short and long... stairmaster gauntlet is just unrelenting, you have to keep stepping up or else. 

a fan might cool them down and make them realise that stepping is easier

Me too. I think they use my sticky Stairmaster model. 

I think what is easy to miss is that, while there will be a reduction in the height needed to gain from one step to the next, the transition force must be applied against a descending step, so it will take a greater force to achieve the same vertical acceleration. As it turns out, I'm pretty sure these two factors will perfectly cancel out, because the actual fixed altitude and speed of ascent/descent of the stairmaster is (to a point) irrelevant, it's the fact that the steps are accelerating neither up nor down that's important, such that life on the stairmaster becomes a frame of reference itself.

I think we agree. For the upper body to remain stationery whilst stepping, the force the leg pushes the body upward, must equal that of gravity forcing it downwards. If it was less, you'd lose height with each step, if more you'd climb off the top of the steps? The equivalent of making or failing to progress fighting an escalator in the wrong direction.

I got to use a quality stepper at David Lloyd during February and was disappointed that the prime unit of achievement was 'floors climbed', with no definition of floor. 17 steps made a floor, steps were 20cm/8 inches as far as I could tell. At 75 steps/min 100 floors took just under 23 minutes and climbed 340 metres, giving 148 watts calculated (168 according to machine) power, at 124 bpm HR. A repeat using 132 floors in 30 mins gave 151 watts and 122 bpm, so fairly consistent.

In Tenerife, a 4km section of steady climb up to Escalona was walked up in 43.5 mins at 127 average HR for 517 metres gain, obviously further and not as steep as the stepper. This equates to 122 watts from the height, plus something for the 4km.

On Great Gable last week, the steepest km went at 120 watts with 118 HR, being pretty tired at the time, for a gain of 316 metres.

All weights have been adjusted for the conditions, rucksac etc.

Personally, I felt the stepper was easier than reality and I still feel the force curves are different shapes for the same averages (you have to accelerate upwards on a real mountain otherwise you don't move) but I am happy to believe the stepper is a decent training device, as long as you don't cheat by loading the handrails like some I saw in the gym...

another analogy maybe the floating backpack- i wonder if anyone's used one on a stairmaster?

youtube.com/watch?v=jqzbU6OTVUg&

Simplistically if you're stepping to remain on-average stationary on a constant velocity descending escalator then you're doing work at least* equal and opposite to the rate of loss of GPE you'd experience when you stop stepping. Which is:

Power = V_vertical x bodymass x gravity (Watts)

*walking on the flat still requires energy, we don't climb 100% efficiently

If you output more than that you'd be gaining GPE, less you'd be losing GPE, either way you'd soon run out of steps on an exercise escalator.

jk

 > youtube.com/watch?v=jqzbU6OTVUg&

I wonder how much they weigh? They conveniently leave this bit off their website.

Kinda pointless for mountaineering as you don't want to lug that extra weight up and the slow movements probably don't result in much benefit, but for running I can imagine this actually helps quite a lot.

Not related at all to a StairMaster but very interesting.

it kind of minimises peak accelerations like the stairmaster- in theory?