Only a couple of pounds resistance will cause the UP step to go down, that is so you are forced to put your weight on the DOWN step which is the one with the full resistance on it.
Yes, the eccentric effort would be decreased compared to walking down real stairs. Try do that activity and tell me if it feels the same as walking down real stairs. By your analysis it should feel exactly the same; I can assure you it will not (and I do remember as a kid trying to do that … not the same as running down stairs at all).
The same resistance works both ways and there is no necessity for the down step to rise at the same rate as the up step lowers - see the video clip linked earlier. Unless you are proposing these function as a see saw … in which case I think you appreciate how the issue of shifting balance such that each 160 pound person has gone up and down 100 times would require less work than would be required to lift two 160 pound people the up distance times 100.
Of course it will feel the same and it does feel the same, I’m a big kid and have walked down the up and up the down stairs recently. As mentioned earlier this is physics 101. Unfortunately frame of reference type problems seem to be ones that you either get or don’t and if you don’t it can be very difficult getting to the AHA! moment.
And in this case, all four of us are correct. If you are descending at a steady speed or maintaining altitude (a special case of “steady speed” in which your speed is steady at zero), then you are exerting 160 pounds of force against the step. If you are descending, then your gravitational potential energy is decreasing, and that energy is being delivered to the step as work. If you are maintaining altitude while the step descends away from you, then your leg is doing work against the step. In both cases, mechanical work is being done on the step; the only difference is where the energy comes from to do that work, either stored GPE or muscles.
That depends on how rapidly the user straightens his leg. Regardless of the descent speed of the pedal/step, it’s entirely possible for the user to straighten his leg at a rate that exactly offsets that descent rate, thus keeping his center of mass at constant altitude. In the end, it doesn’t matter: the pedal sees 160 pounds of force the entire time it’s moving down. You can do work on the pedal directly by straightening your leg just fast enough to offset its descent rate, or you can step up rapidly to increase your GPE, and then let that GPE get converted to work on the pedal. Either way, your muscles did the same amount of work.
You have this notion of “uphill” exercise. Exercise is mechanical work - force applied over a distance - regardless of whether you move your body uphill against the force of gravity, move something else downward against a dissipative mechanism or moves something else sideways against some other sort of dissipative mechanism. The math is exactly the same in every one of those cases: W = F * d. Whether you push your 160-pound body upward through 12 inches or push a step downward through 12 inches with 160 pounds of force while you stay at the same altitude, it doesn’t matter: in either case you’ve done the same amount of work, your muscles have burned the same amount of sugar, you’ve gotten the same amount of exercise. The only difference in all these cases is where that work ends up, either in a brake or in your increased GPE.
There is no “if”; walking up a hill does require you to exert energy. How much depends on your weight and how high you climb: W = F * d. Have you noticed that you get out of breath walking up a steep hill, but not walking down that same steep hill at the same speed? You get out of breath walking uphill because you are doing mechanical work to raise your GPE; the energy to do that work comes from your muscles burning sugar, and you breathe harder to get more oxygen to make that happen. Going downhill, your body is now absorbing energy instead of expending it, so you don’t breathe hard at all.
I apologize for not explicitly describing what I meant by “stationary.” My original statement was this:
By “stationary”, I meant that your center of mass was not moving. If the escalator is descending away from you while you are maintaining a constant elevation (by walking up the steps at a rate that exactly offsets the speed of the escalator), then you are exerting 160 pounds of downforce on the steps. No object in a gravitational field can remain at a constant altitude without exerting a downforce equal to its weight against some other thing. This is true regardless of whether that other thing is moving or not. Example, a 2000-pound helicopter in hover exerts 2000 pounds of downforce on the air that is moving downward through its rotor disc.
Still thinking about this . . . Despite my massive intellect being packed into a very finite-size brain (a.k.a. “Density”) 
. . . There’s still something I’m missing. There’s still some AHA! moment that hasn’t happened yet.
Everything that Machine Elf and Richard Pearse are saying about the action/reaction of that 160 lb. seems right. I understand all that (quite clearly, I think). But I’m sort of thinking that your arguments, however correct, are somehow incompete – something is missing.
Or, to put it another way, all your explanations seem to not quite addressing my question or my lack of understanding.
Let’s see if I can bring some focus towards the “missing piece”.
I understand about the 160 lb. But, as I and DSeid *and Machine Elf are all saying, that’s a constant factor. My downward-pushing 160 lb. is constantly there opposing the upward-pushing of the ground beneath me, regardless of whether I am . . .
[list=“a”][li] Standing still on level ground;[/li][li] Walking on level ground;[/li][li] Standing still on an inclined place (hillside, inclined treadmill, or non-moving escalator);[/li][li] Walking uphill on a stationary staircase or hillside;[/li][li] Walking up the down escalator, raising my CoG;[/li][li] Walking up the down escalator, holding my CoG altitude constant;[/li][li] or even (approximately) dangling from a slowly-descending parachute.[/list][/li]Yet walking uphill is a much more intensive exercise than walking forward on level ground. If we factor out all the factors that make it any exercise at all to walk on level ground (factors that are also present walking uphill), then we are left with the relevant, and major, factor: The work involved in raising my CoG as I walk up the hill. This must be something substantially more than the work of just standing still (which is exactly 0).
So I want to factor out the 160 lb action/reaction, and ask what the relevant difference is when walking uphill. What is the additional effort going on there? But wait, that’s exactly the work of “pushing against gravity” with my 160 lb. Oops. Can’t factor that out after all.
I am still being bothered by the apparent paradox here, because there’s still something I’m missing.
As Chronos put is most succinctly a few posts back, my motion walking “up” the escalator is the same, with respect to the escalator, regardless of whether I’m gaining altitude with respect to earth, or staying in the same spot walking up the down escalator. I am counter-arguing that walking “up” w.r.t. the steps is not the source of the high-energy uphill work-out here in the first place. Rather, walking “up” w.r.t. the earth and its gravity is the source of the high-energy uphill workout, and requires that I really and physically gain altitude for that to happen. The movement of the steps, absorbing my downward-pushing 160 lb., however accurate, seems to be a red herring here. I’m still failing to wrap my mind around why that’s relevant.
Thus, I’ve attempted (somewhat speculatively) to theorize that the kinetic energy that I’m pouring into the brake must be (approximately) just the energy that I would have used walking on level solid ground. After all, when I walk forward on level ground, my 160 lb. vs. the upward-pushing 160 lb force of the sidewalk keeps me at constant altitude. (Disclaimer: May not work out this way if you’re a Corvette.)
And, from that, I’ve theorized from first principles (my first principles, that is) that the constant-altitude-CoG scenario on the Stairmaster must occur only when the brake resistance is dialed down to about level-ground-walking resistance. Otherwise, it seems like I’m a few First Principles short of a Complete Theory here. (But hey, at least I was on the right side of the 0.999… = 1 argument!) To get the uphill exercise, some effort more than that must be required.
I’m seeing some additional “factors” might be in play here – complicating factors – that I’ve been trying to avoid all this time. More on that in another post, when I compose my thoughts.
Thank you for all the discussion, by the way. Notwithstanding the above, there’s already some ignorance being fought here, with the ignorance already suffering heavy losses. But ignorance hasn’t been totally defeated yet! At 86 posts (and counting), it’s taking longer than we thought!
I’m seeing two more factors – perhaps messier factors – that we’ve been madly trying to avoid.
First, the work-over-distance factor or something like that. Second, the work-over-time factor or something like that.
Note that I’ve used the term “exercise” as being synonymous to “work” sort-of, except for it being non-synonymous. Maybe we need to bring real-life exercise physiology into the discussion (about which, I know zilch).
Start with W = F * d. If I use a lever to help lift a weight, what is it doing for me? I can just barely lift a 30-lb weight directly. But with the help of a lever, I can lift it easily. If I can easily lift the weight 2 ft. with the help of a long lever, I’ve done 60 ft-lb of W, right? Am I burning the same calories whether I lift it myself or use the lever? Lifting it directly sure seems like a lot more small-w “work”, even if these two scenarios (with lever and without) accomplish the same amount of Big-W Work. What would Archimedes have said?
The point being: There are different ways of doing the same W = F*d work that seem to require very different amounts of muscular effort, and which deliver very different degrees of cardiac exercise.
Is there something here that’s relevant, or at least analagous, to the discussion of climbing up stairs vs. walking up the down escalator with constant CoG?
Second, it is pointed out above that Scenario A or Scenario B might be determined, not only by the resistance of the brake, but by how quickly I straighten my leg. I knew that, but I was really trying to ignore it. The question must be asked though: How is the difficulty of the exercise related to the speed of the exercise? If I walk up a hill very slowly, it seems easy, although time-consuming. If I walk the same hill very rapidly, I get very breathless very quickly, and drive up my pulse rate. But have I just burned the same number of calories? Technically, haven’t I just done the same amount of W = F * d work?
Clearly, the muscles can only turn glucose and oxygen into energy at a certain maximum rate, and the blood can only deliver oxygen at a certain rate. But Machine Elf points out that no matter how slowly the steps descend, I can match that speed in straightening out my leg. Does the speed of the action on the Stairmaster become a relevant factor? Again, I could walk up a hundred stationary steps slowly with great ease, but climbing rapidly gets me breathing hard, while (ultimately) burning the same amount of glucose, accomplishing the same W = F * d. Is there something here that need to get factored into the Scenario A vs. Scenario B discussion?
Note the vagueness of these questions, the way I have worded them. That is as intended, accurately portraying the clarity of my thoughts about these factors.
This is what you keep missing. You keep thinking about one foot at a time. There isn’t one pedal going down. Both pedals are sinking! If you only shift a couple of pounds to the up foot, then the down foot will hit the floor. If you let a pedal bottom-out, then you’re doing it wrong. That’d be like putting down the dumbbell just before lifting your arm…that’s not how the exercise is supposed to be done.
Your full body weight is on both pedals, total. You have to keep your entire body up, not just one foot.
I think I might see what’s missing in your train of thought as you try to distinguish between walking on level ground and walking uphill. In the equation W = F * d, the only d that’s relevant is the portion of it that’s parallel to F. Example:
-you walk 12 inches across level ground. Gravity is pulling you vertically down (F = 160 lbs), but you are moving horizontally, so the portion of d that’s parallel to F is zero; you’ve done zero work.
-you climb 12 inches up a ladder. F=160 lbs vertical, and now your movement was entirely parallel to that force, so d = 12 inches. You’ve done 160 lb-ft of work, and raised your GPE by that much.
-you walk 12 inches up a 45-degree slope. F = 160 lbs vertical, but your 12 inches of movement was at a 45 degree angle to that force. So the portion of your movement that was parallel to F is cos(45 degrees) * 12 = 8.49 inches (draw this on paper, and you’ll see that by walking 12 inches up a 45 degree slope you’ve only increased your altitude by 8.49 inches). So you’ve done 160*8.49 = 113 lb-in = 9.43 lb-ft of work, and raised your GPE by that much.
If that detail (work is the dot product of the force and movement vectors, rather than their simple multiplicative product) is what was missing, then maybe that helps you understand why you get out of breath walking uphill but not when walking on level ground?
W = F * d. You push down on the step (and the step pushes up on you), the step moves 1’ away from you, you’ve done work. You push down on the step (and the step pushes up on you), you move up 1’ away from the step, you’ve done work. You push down on the step (and the step pushes up on you), you move up six inches, the step moves down six inches, you’ve done work. In all three cases, you’ve done the same amount of work, you’ve gotten the same amount of exercise.
If you change your frame of reference, maybe it’ll help clarify things. One of the tenets of physics is that you can examine a kinematic problem like this from any non-accelerating frame of reference, and the forces and energy exchanges all work out the same. This is why, for example:
-playing a game of ping-pong on a cruise ship doing a steady 20 knots feels exactly like playing ping-pong in your basement, and the ball behaves exactly the same way.
-sitting in your seat in an airplane cruising at a steady 500 MPH feels exactly like sitting in the same (uncomfortable) seat in your living room.
-standing in an elevator when it’s climbing (or descending) at a steady 20 MPH feels exactly like standing in the lobby. In a really smooth elevator, once it stops accelerating (and before it starts braking), you can close your eyes and you won’t even know you’re moving.
That last example is particularly interesting. Imagine you’re in an elevator that is descending at a steady 1 foot per second (don’t ask me why it’s so slow). Inside this elevator is a concrete staircase with 1-foot-tall steps. You begin climbing this staircase, taking one step per second. An observer standing in the elevator with you sees that you have increased your altitude relative to the floor of the elevator. From his frame of reference, it appears you’ve done some work. And indeed you have, although an observer standing in the lobby will report that your altitude relative to the lobby floor didn’t actually change as you went up those steps; from his frame of reference, it looks like you’re walking up a down-moving escalator. But you did do some work, and that’s true regardless of whether the frame of reference is stationary with respect to the earth, or stationary with respect to the steps that are moving down beneath your feet; the work you did went into pushing the elevator down, with the elevator’s electric hoist motor acting as a brake to absorb that energy. Inside the elevator, your leg doesn’t know whether you were actually climbing relative to the earth or not; your leg is blind, and it only knows “I pushed with 160 pounds, and I straightened 12 inches”. To your leg, it feels exactly like walking up the fire escape stairs.
Astronauts in orbit could use a Stairmaster and get exactly the same workout, if they had bungees attached to their waist or shoulders pulling them toward the base of the machine with 160 pounds of force. Their leg says “I pushed with 160 pounds, and I straightened 12 inches,” just like your leg did in the aforemented elevator, and just like your leg did in the gym down the street.
Hopefully my earlier explanation (work is the dot product of force and distance) helps explain why this is not true. Note that a bicycle can coast forward on level ground for a great distance (subject only to the sad reality of rolling resistance and aerodynamic drag), showing that there isn’t inherently any work required to move horizontally when gravity is pulling you straight down, but a bicycle won’t get very far up a steep hill without you doing some work on the pedals.
Any time you’re working out on the stairmaster, the force you exert on the pedals exactly equals your body weight; if this were not true, you would accelerate up or down, eventually hitting the floor or hitting the upper travel limit of the machine. Changing the “resistance” setting of the Stairmaster changes the speed at which the pedals/steps move when you apply your body weight. The constant-altitude scenario occurs whenever the operator moves his legs at a speed that exactly offsets the speed of movement of the pedals/steps, regardless of whatever that speed may be.
“Work-over-distance” is possibly a meaningless term. If you really wanted to ascribe meaning to it, it would just be force: W = F * d, therefore W/d = F.
“Work-over-time” is mechanical power. It is force multiplied by speed (instead of just distance): W = F * d, therefore W/t = F * d/t, where d/t = speed. Climbing up a given number of steps requires the same amount of energy no matter how fast you do it. But if you want to do it twice as fast as you did previously, you will need to generate twice as much mechanical power (albeit for half the time).
If you use a lever to provide you with a mechanical advantage, you decrease the amount of force you need to exert, but if you examine the geometry of it, you’ll see that you have also increased the distance that your end of the lever moved (compared to the other end of the lever). The two effects exactly offset each other such that the work you supply at one end of the lever is exactly equal to the work received at the other end of the lever. The law of conservation of energy says that this absolutely must be so, but you can also prove it by examining the geometry of the situation.
Consider a 1000-pound weight. You attach it to the end of a 51-foot horizontal lever so that the weight is 1 foot from the fulcrum; you’re on the other end of that lever, 50 feet from the fulcrum. If you want to hold that weight off of the ground, you need to press down on your end of the lever with 1000 * 1/50 = 20 pounds of force.
Let’s try raising that weight. You push your end of the lever down 1 foot, doing 20 lb-ft of mechanical work. Because of the vastly differing lengths of lever on each side of the fulcrum, the short end of the lever only moves upward 1/50 of a foot. Having borne a force of 1000 pounds through that distance, the lever has delivered 1/50 * 1000 = 20 lb-ft of mechanical work to the weight - exactly the amount you provided at the other end.
You’ve done the same amount of mechanical work, it’s just that you’ve done it more quickly. You produced more power (same mechanical work provided in a shorter time). Work is energy transfer, so if you’re going to do mechanical work more quickly, your body needs to supply energy at a more rapid rate than it did when you were walking: you breathe more rapidly to get oxygen at a faster rate, and your blood flows faster to bring fuel and oxygen to your muscles at a faster rate - but it does so for a shorter period of time (since you got to the top of the hill faster).
Yes. in fact, it is the relevant factor in the intensity of the workout. When you choose a “higher intensity” workout on a stairmaster, you’re changing the speed, not the force. The force is always your weight (as long as you’re not pushing down on the handrails). If you spend twenty minutes on a Stairmaster at high speed, you’ve moved the pedals farther than if you had set it to a low speed. Since the force was the same (your weight) in either case, setting it to a high speed means you’ve done more mechanical work in the same amount of time. More power, more intense workout.
Wow, this has turned into another airplane on a treadmill thread. What is it about tradmills (and stairmasters and escalators, natch) that breaks physics in some people’s heads?
I went and measured the return spring on the stairmasters at my local gym today- some of the people above said that would make a difference vs real stairs etc. It takes approximately 15 lbs to keep one step from rising at all (ie, it took 15lbs of weights to hold the step down after pushing it down). The return spring holds more weight at the very bottom than near the top, but the difference was less than 5lbs. The weight on the step impacts the speed though, so at higher levels you can’t leave anywhere near 15lbs on the “going up” step or it wouldn’t come up fast enough for you to step back down on it. Still, I see the stairmaster potentially taking up to 20-25lbs of your weight, at slower speeds (up to 15lbs on the “down” side and 5-10lbs on the up side, as you have to be under 15lbs to get the step to go up at all). That is more significant than I would expect but still reasonably comparable to going up steps at a similar speed.
Thanks! 
If the ascending pedal is bearing 5-10 pounds of your weight (to keep it from slamming all the way up), then the remainder of your weight is applied toward performing work on the descending pedal, regardless of how much of that work goes into loading the return spring and how much goes into the brake. If your right leg is moving upward (or holding its pedal steady) with a 5-pound assist, then your left leg is pushing down with 155 pounds of force instead of 160 pounds, and so your left leg is doing 97% of the mechanical work that it would have been doing without the right leg receiving that 5-pound assist. If we say the return spring offers ten pounds, then the down-moving leg is still doing 94% of the work it would have otherwise doing.
TL,DR: in terms of cardiovascular exercise, using a stairclimber at a given pedal speed is almost like climbing real stairs at that same speed. If you’re very heavy (250+ pounds), then the difference becomes negligible.
Note that this is independent of the discussion about whether using a stepmill is exactly like using concrete stairs.
AHA! (Wait, did I just say that?) This begins to approach something I can wrap my mind around. Climbing stairs in the elevator, as observed by a bystander in the elevator, is the easy-to-picture “frame of reference” here. The more difficult part to picture is: Why an observer on the ground sees the stair-climber doing any work. (After all, he sees the climber at a constant altitude.)
I’m starting to get a picture of what I’m maybe missing – it’s isn’t exactly about misunderstanding vertical components and horizontal components or slant-height. It’s more elementary, and I suspect a big stumbling block for non-physics-students:
If I stand my 160 lb on a sidewalk yet don’t plunge to the middle of the earth, it’s because the sidewalk is pushing up on my feet with an equal 160 lb, right? (Corvettes excepted.) Then what happens if I stop pushing down with 160 lb on the sidewalk? What happens if I step off the sidewalk? Why doesn’t the sidewalk spring upward into the sky (or at least a few inches)? This (or similar) must be something that beginners ask a lot. I suppose the answer is that cement is very stiff, and pushing down on it with 160 lb, or not, moves the cement vertically by only a few molecules’ distance, maybe. IOW, the person’s 160 lb weight, by any practical measure, is insignificant and thus too easily overlooked.
As applied to the descending elevator: Tell me if I’m getting closer on this: The observer on the ground sees the elevator descending, under control of a motor, whether there’s a 160 lb person in it or not, and whether that person is walking up the steps or just standing still. If he’s pushing the elevator downward 160 lb by climbing the steps, is this just too easily overlooked because it makes such a small difference in the elevator’s motion? (This is kind of like asking: If a housefly ascends a Stairmaster, is it doing any work?)
In fact, they’ve got that space treadmill up there – The Combined Operational Load Bearing External Resistance Treadmill, or C.O.L.B.E.R.T. device. So there’s one treadmill that DID take off! I wonder how the users use it.
Now this leads to a decidedly unexpected and counter-intuitive result: As you discuss here, the intensity of human exercise is based on power expended, rather than just amount of work accomplished. (Am I saying that right? If not, can you figure out what I’m trying to say?) Normally, one would expect to get a more intense work-out by setting an exercise machine to higher resistance. (How it works with a stationary bicycle, e.g.) But with the Stairmaster, though, it looks like you have to run up the steps faster to avoid bottoming out, thus getting a more intense work-out, by setting it to a lower resistance. This is the scenario in which it takes all the running you can do just to stay in one place. Setting a higher resistance, you move slower to stay in one place, giving an less intensive work-out over a given time-period. (Or, you could climb faster and work harder, but then you’d ascend and overrun the top of the steps.) Is that right?
To the observer on the elevator, it looks like the climber has pushed himself up 12 inches while the floor didn’t go anywhere.
To the observer in the lobby, it looks like the climber has pushed the elevator down 12 inches while staying at the same altitude.
To the leg muscles of the climber, it looks like the climber pushed and straightened his leg 12 inches, and they don’t care which end (hip, or foot) actually moved relative to the earth.
Sit on the floor with your back against the wall, and use your leg to push your desk 1 foot across the floor. The friction between your desk and the floor requires your leg to exert a force, and you moved it through a distance. Nobody changed elevation at all, but your leg surely did some work.
It’s all the same thing: W = F * d. There was force, and that force pushed through a distance.
Correct. This is an example of Newton’s third law: when body A exerts a force on body B, body B also exerts an equal and opposite reaction force against body A.
If your legs stop exerting 160 pounds of force against the sidewalk, your body will begin to accelerate downward under the influence of gravity. When people faint, their muscles relax; their legs stop pushing down on the floor, and they accelerate downward.
Yes, exactly. There’s an entire subdiscipline of engineering called mechanics of materials, part of which deals with the fact that all materials - even the concrete from which sidewalks are made - are elastic to some degree. That is to say in order for any material to exert a force, it must deform, even if only very slightly. Step on that sidewalk, and there’s a microscopically deep depression where your foot is pressing down (and the dirt under the slab is likewise very slightly compressed). Step on a foam rubber mat, and the distortion is much more obvious; it has to deform to a far greater degree before it’s able to exert a reaction force of 160 pounds.
Even water, which is widely understood to be incompressible, is actually compressible to a very, very small degree.
Newton’s first law says that for an object moving at a constant speed, the sum of all forces acting on it equals zero. So if a fellow is standing on the floor of an elevator that’s descending at a steady speed, the sum of all forces on him must be zero; gravity pulls him down with 160 pounds, so the floor of the elevator must be pushing up on him with 160 pounds, so Newton’s third law says that his feet must therefore be pushing down on the elevator floor with 160 pounds.
If he’s climbing up steps as the elevator descends such that his speed relative to the earth is a constant zero, then once again the sum of all forces on him equals zero Gravity is pulling him down with 160 pounds, the elevator is pushing him up with 160 pounds, so again, his feet must be pushing down on the steps with 160 pounds.
Video here. She has to use a harness to pull her body downward against the tread in order to get traction. However, in the case of The C.O.L.B.E.R.T., in which the harness pulls the user perpendicularly toward the tread, the intensity of her workout isn’t particularly governed by how hard the harness pulls on her; it’s governed by how fast she runs, i.e. how fast she’s flinging the mass of her legs back and forth. It takes a lot of power to accelerate your rear leg forward rapidly, and then accelerate your front leg backward just before you plant it on the ground. This is why jogging on level ground leaves you breathing hard, but walking the same distance on level ground does not.
Yes. A bicycle rider who can sustain a higher speed is putting out more mechanical power than someone who can’t sustain as high a speed. Tour de France riders average around 250 watts of power output. The watt is the SI unit of power; 250 watts is 0.335 horsepower, which in turn is 184 lbf*ft/s. Assuming one of these riders weighs 184 pounds, he (and his steroids) could theoretically climb a staircase at a sustained vertical speed of 1 ft/s. This doesn’t sound like much if you’re just going from first to second floor, but try keeping it up for 3+ hours without stopping.
A human being can actually put out far more power than that, but not for long. Example, sprinters get an extremely intense workout, but it only lasts about ten seconds. They’re not dealing with much aerodynamic drag (they only hit 25 MPH at the very end of their run; TDF riders average 30+ MPH for hours at a time), but they’re forcibly flinging the mass of their legs back and forth as fast as they can, and that takes a lot of power.
With a stationary bicycle (or a moving bicycle), you have the option of adjusting the speed or the resistive force of the pedals (or both) to suit you. On a moving bicycle, the forward speed of the bike determines the power requirement:
P = F * d/t (where d/t = speed)
F = drag force, which is proportional to the square of speed (due to the nature of aerodynamic drag)
So on a moving bicycle, you go faster to increase the total power requirement, and you can select different gear ratios to change the relationship between pedal force and pedal RPM. If you’re maintaining a given forward speed, using a lower gear means you pedal faster but with less force, and using a higher gear means you pedal more slowly but with higher force (this is somewhat analogous to the lever example discussed upthread). Either way, it’s the same power output from your legs because the power requirement is determined by the forward speed of the bicycle.
On a stationary exercise bike, you select different pedal-force vs. RPM relationships on the control panel. An “easy” setting means pedal resistance force doesn’t increase much as pedal RPM increases, and a hard setting means pedal resistance force goes up very quicly as pedal RPM increases. At any one of those settings you can vary your pedal RPM as you desire, but you’ll need to alter how much force you apply to the pedals in order to operate at a different RPM. You are able to change how much force you apply to the pedals because some of your weight is also supported by the saddle and/or handlebars; if you apply more of your weight to the pedals, then less of your weight is applied through your hands and butt.
Yes, exactly. On the Stairmaster control panel, you select different “pedal-force vs. pedal speed” relationships, but it is inherent in the operation of the machine that you will not be able to alter how much force you apply to the pedals; you have to apply exactly your weight. The machine then spins up to whatever speed causes it to apply 160 pounds of reaction force to the pedals. The only way around this is to cheat by putting some of your weight on the handrails, leaving less weight to be applied to the pedals (the handrails are supposed to be used just for balance/safety). Alternatively, you could fill your backpack with 40 pounds of bricks so you could then apply a total of 200 pounds of force to the pedals.
Here’s a real-world example, the annual Willis Tower Stair Climb event. In 2010 Jesse Berg, a 150 pound man, won by climbed to the top (1353 feet) in just 13 minutes, 46 seconds. That’s 202,950 lb-ft of work in 826 seconds, for an average power output of 246 lbft/s. That’s significantly more than the aforementioned TDF rider (184 lbft/s), but it was only for about fourteen minutes; he would not be able to keep up that kind of output for several hours. My hypothetical TDF rider would take 23 minutes to climb the Willis Tower - but then he could climb it again that fast ten more times in a row without taking a break.
Again, Machine Elf, thanks very much for your patience and discourse. Notwithstanding this . . .
. . . I’m learning a lot here, and this thread is very much doing the “work” that a SDMB GQ thread is supposed to be doing. (Try to express that in ft*lb ! )
Perhaps you’ve figured out, from my comments and questions, what my background is:
[ul][li] NO coursework whatsoever in physics (beyond a long-ago high-school class in which I learned approximately nothing);[/li][li] Sporadic exposure to discussion (via reading or listening) of physics principles (much of it, recently, here on SDMB);[/li][li] However, I do have the math, up through: 3 semesters Calc + 1 semester Diff Eq, plus statistics and Finite Math, with straight-A++ in all of that. (However, all that was 20+ years ago.)[/li][/ul]
So a lot of what you’ve been covering is stuff that I’ve vaguely understood, but never much thought about in any applied context. This whole conversation has been very helpful in clarifying and somewhat extending my understanding of this stuff. As I mentioned way upthread, your discussions are pretty much at just the right level for me.
(As you pack more knowledge into my finite-volume brain, does that mean I become denser?)
At this point, I think we can either begin to wind this thread down, or continue to talk more about things like exercise physiology, e.g., walking vs. jogging; level vs. hill-climbing vs. stair-climbing, etc. On that topic, we’ve sort of more-or-less covered the questions I had envisioned asking.
I’m interested in just what exercise there is in, say, walking on level ground. The very biggest component of uphill hiking, namely the vertical, is totally absent. I think you’ve pretty much covered that, but let me ask: Then, is the major component of level-ground walking in the effort of swinging the legs back-and-forth, as opposed to various kinds of friction involved? Is there also an intra-muscular friction or other “wasted” effort? (To the extent that exercise jacks up your body temperature, this must be true, right?)
Up-hill hiking has always seemed, to me, to be a much better exercise than level walking. And I think there’s an additional component besides just the vertical ascent. The “lift” of straightening your leg comes at a phase of the stepping cycle that is totally absent in level walking, and almost seems to involve muscles that aren’t even involved in level walking, and also involves joint movement in ways that level walking doesn’t. (Try walking up a hill backwards sometime. See if that doesn’t involve muscles you didn’t even know you had!) I’ve always found uphill hiking to be, simultaneously and paradoxically, much more intense and much more gentle at the same time!
These are the sorts of things I was thinking of exploring with my original OP here, in which I focused on asking how well a Stairmaster simulates climbing up a hill or up fixed steps.
Not exactly. Climbing stairs is much more aerobically challenging and puts more stress on the knees. Stairmasters can be adjusted to levels that are more or less challenging. One still gets a good workout on the stairmaster but it takes longer than climbing stairs. I am 60 years old and have been working out for many years and with age problems with knees and hip joints often occur as I have experienced. I prefer the eliptical machine and spinning, swimming and other low impact exercise because it is safer for me. If you are young, enjoy your abilities now but realize if you do as I did and do extreme running and other high impact exercise you may pay for it in later years. Good luck.
Okay. Thinking about it some more I can buy the escalator style stair climber with small caveats - most everyone holds on to some degree which does change things some, and I wonder about the acceleration/deceleration events being different between the two circumstances.
The pedal style is still something that seems a different beast. It seems that the pedal pushes up with about 25 pounds at a basic set level of resistance at rest. Obviously the down resistance is different. The explanations offered so far seem to claim that it is the same work out if there is hardly any resistance or very high resistance, the only factor being how many steps of what distance are taken. And I still don’t accept that.
Another issue is that physics work and muscle work are not the same thing. Our bodies our not perfectly efficient machines and different sets of movements at different speeds have wide ranging different efficiencies of producing physics work from muscle work (calories). The kinematic differences should not be dismissed lightly. FWIW (and possibly not much as I cannot find where they got their information) this site lists, for my weight, machine stairstepper at hard effort to be a relative 649 calories an hour to running up stairs at 987.
Still digesting Machine Elf’s latest posts, in particular #94 above. And, in particular, and I already said, the scenario of the fixed staircase in the elevator got me pretty close to the AHA moment. As I’ve been thinking about this all day, I sort of feel like I’m pretty close to seeing the final missing loose ends.
Going back to the Recumbent Canoe scenario I posited a while back, with resistant pedals to push on while you lie horizontally on your back: You get your exercise pushing the pedals. But your body doesn’t slide backward in the canoe because of friction. If it were a frictionless canoe inside, you would just slide backward, getting your exercise basically from moving your own body mass, rather than the resistance of the pedals.
But suppose you put your arms up above your head (meaning, toward the back of the canoe) and pushed against the back of the canoe while you pushed on the pedals with your feet. Now, your body doesn’t move back, and instead your feet move the pedals and you get the exercise from that.
So I posited, a ways above, that you stood on a Stairmaster in a room with a low ceiling and pushed up on the ceiling while pushing down with your feet. THEN you get the exercise of pushing down on the steps, as Machine Elf has been saying all along. Except he says you are getting that, even without pushing up on the ceiling!
Now I’m seeing what’s wrong with the above picture. Picture that C.O.L.B.E.R.T. treadmill in the ISS again. The user needs a harness (I gather that’s some kind of bungee cord?) pulling down to get traction with the tread. That’s like pushing your hands up against the ceiling. But come down to earth, and gravity is doing exactly that for you. So your 160 lb of downward force under gravity is performing that role, in place of you pushing up on the ceiling in order to produce that downward push on the steps. Looking at it that way, I’m now seeing that viewpoint as the last missing loose end I need.
How about it, Machine Elf? NOW have I finally got it all together correctly, or is that analysis still all messed up?
It has to be. You have to do mechanical work to accelerate the mass of your rear leg forward; your muscles oxidize fuel to make that happen. When your rear leg comes to the fore and you slow it down just before planting it, your muscles are absorbing mechanical energy - but they don’t generate fuel and oxygen in that process; you can’t “undo” aerobic exercise lke that. Conservation of energy says that the work they absorb doesn’t cease to exist, though, so the only other real option is that this absorbed work gets dissipated as heat (more on that below).
Note that the same thing happens your forward leg. Just before you plant it, you accelerate it so that your foot matches the speed the ground is going by, and then after you pick it up at the end of its stroke, you brake it, wasting its kinetic energy - and now it becomes the rear leg, ready to be accelerated forward as described above.
If you are walking, your slow-swinging legs don’t have much kinetic energy in them at mid-swing, i.e. your muscles aren’t doing a whole lot of mechanical work to accelerate them. If you are running, your legs are moving very fast at mid-swing. Each leg stroke represents a LOT of mechanical work that you’ve done which then gets pissed away as heat when you bring that leg to a stop just before planting it.
Just like car engines or steam turbines, muscles are not 100% efficient. They derive energy from fuel and oxygen, and only a portion of that becomes mechanical work; the rest is waste heat. This is why you get warm when you exercise, and it’s why shivering is usually a useful response to low body temperature (shaking your body back and forth generates waste heat, which is pretty handy when you’re bone-ass cold). And it’s why walking up a steep hill gets you sweating: in addition to the modest aerobic activity of walking, you’re now also doing the mechanical work of moving upward against the influence of gravity. In switching from walking on the level to walking uphill, your mechanical power output has increased just as surely as if you had switched from walking on the level to jogging on the level.
So why don’t we get hot when we absorb mechanical work? Why doesn’t walking downhill make us hot and sweaty like walking uphill does? This points to how inefficient the human body (as a whole) really is. Wikipedia says muscles are about 22% efficient, although this includes the 40% efficiency of converting food to muscle fuel. This means that from the energy delivered to the muscle as usable fuel, only about half of it gets converted to mechanical work, and the other half gets dumped into the body as waste heat. I’m pretty sure this 50% efficiency is for the muscle alone, and doesn’t include the waste heat generated by the cardiovascular activity that supports your leg muscle’s work output. Start jogging, and pretty soon your heart is doing a lot of work to keep blood moving through your body, and your diaphragm is doing a lot of work to keep air moving in and out of your lungs; these things generate a fair bit of waste heat as well. If you’re walking downhill, your muscles aren’t doing mechanical work against gravity(they’re absorbing it), so they aren’t demanding fuel and oxygen from the rest of your body - or at least not any more than when walking on level ground - so your cardiovascular system isn’t burning a ton of energy trying to keep fuel and oxygen supplied to your legs. The only real waste heat is the gravitational potential energy that your legs are absorbing as they keep you from speeding out of control while descending the hill, and that’s not much compared to the waste heat created when your body is trying to produce mechanical work.
I’ve been avoiding such physiological details, trying to focus on physics and the concept of mechanical work, but you and Dseid are right: the details of which muscles are doing the work, how hard they pull, how far they move, and how fast they move are relevant. I recall reading years ago that a bicyclist gets best efficiency when the pedals are spinning somewhere around 90 RPM. And indeed, if you watch the Tour de France or any other competitive cycling event, you see that the pedals make a complete revolution about three times every two seconds (the exception comes when they’re riding so damn fast that they don’t have a higher gear available). Pedaling faster with less force produces the same mechanical power output, but is apparently less efficient; the same is true when pedaling slower with more force. Taking the latter case to an extreme, you get to a power lifter who is squatting with several hundred pounds on his shoulder, and lifting very slowly; he can’t keep that up for very long at all before his leg muscles are wiped out.
So yes, although I’ve been arguing that mechanical work output is the same when you exert X force through Y distance regardless of one’s frame of reference and direction of movement, the physiological details of how a human body gets utlized for doing that mechanical work certainly do affect energy input requirements.
Yes, exactly. As I said upthread, gravity never takes a break. It’s always pulling down on you with 160 pounds of force, and if you’re not accelerating downward (this could mean you are stationary or it could mean you are moving up/down with constant speed), then Newton’s first law says that something else must be pushing up on you with 160 pounds of force, in which case Newton’s third law says that you must be pushing downward on that thing with 160 pounds of force.