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This question is inspired by a sign I saw at a lift, which said something like:

Going up 1 floor or down 2 floors? Take the stairs, it's better for your health and for the environment.

There's no doubt that taking the stairs is better for one's health, but the physicist in me wonders about the latter. An analysis:

  1. Presumably whoever wrote that sign was thinking about energy usage. By taking the stairs instead of the lift, I save on the electricity required to power the lift.
  2. However, gravity is a conservative field. The end result in both cases is that I move up one floor, so the amount of work (i.e. energy) required to get me up one floor is independent of the path I take. It should only depend on the initial and final states. Therefore, the electricity saved is compensated for by the fact that I need to eat more food (so my muscles can produce the energy required to move me up one floor).
  3. If I take the stairs, I do more than $mgh$ of work, because the stairs isn't completely vertical and there's some amount of horizontal work done. Therefore it's actually more energy-intensive overall to take the stairs instead of the lift. (There is also some kinetic energy I have to impart to my body to make it move upwards, but my body also has kinetic energy in the lift, and we assume they are equal.)
  4. However #3 seems superficial because the final state isn't exactly the same: the lift has also moved up one floor. The mass of the lift is obviously quite large, so to get it up one floor takes more energy.
  5. But it's exactly because of this that modern lifts use a counterweight that serves as a gravity battery. Whenever the electric motor moves the lift down, some amount of weight is lifted as a counterbalance. When the lift moves up, most of the energy comes from the potential energy stored in the gravity battery; the electric motor doesn't actually do much work. Besides, even if the electric motor does more work, the argument only holds in one direction. If it takes more energy to go up the building (compared to walking), it takes less energy to go down the building (compared to walking).
  6. If we assume that on average I move both up and down the building, then this difference cancels out, and we're left with the argument in #3.

Conclusion: the sign is wrong. It's (slightly) worse for the environment to take the stairs instead of the lift.

I'm wondering if this analysis is good or if I missed something.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – rob Oct 11 at 20:18

10 Answers 10

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I follow your analysis but not your conclusion. You are missing two key points, which as far as I can see might outweigh all the other points you mention:

  1. You must compare the efficiency of the electric engine running the lift with your body-"engine".

  2. You must compare the "fuel" that the electric engine and your body-"engine" use.

To the first case, all your other points pale and are negligible, if an old inefficient engine is in use, or opposite if you as the person walking up the stairs have a hard an inefficient time doing so.

To the second case, what if the electric engine is run by the roof solar panel, geothermal heating or a local wind turbine? Then the elevator's impact becomes negligible*. On the other hand, if you eat, drink and gain nutrition in an environmentally sustainable manner**, then your impact might be considered negligible.

These thermodynamic and fuel-production factors*** are, as far as I can see, more important than your presented analysis, which is based purely on mechanical energy.


* Unless we include an analysis of the lifetime, production and disposal of the solar cell, geothermal plant for wind turbine, in which case they will never win with current development technologies. We with then also have to consider other uses of these sources, and the math quickly becomes large and complicated.

** Home-grown vegetables etc.

*** I'm sure we can find more such factors if we dig deep into the details of the lift technology and human physiology. The environmental-impact-math will also highly depend on how we estimate and evaluate indirect factors that may make all of your and my points moot, some of which are mentioned in comments and other answers, such as the energy storing capability of a lift's counterweight or such as the question of if the lift will be implemented and in use regardless of what you choose to do due to regulation and accessibility for the disabled/elderly.

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    $\begingroup$ Not to forget production, installation and disposal of an unnecessary elevator... $\endgroup$ – I'm with Monica Oct 10 at 14:41
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    $\begingroup$ @AlexanderKosubek This argument might be a case of the sunk cost fallacy: When the elevator is already there, then the ecological footprint of producing, installing and disposing will happen regardless of whether it's being used or not. These cabon costs might be relevant when considering whether to install a new elevator or not. But they are irrelevant for deciding whether or not to use an elevator which is already there. $\endgroup$ – Philipp Oct 10 at 14:46
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    $\begingroup$ @Philipp The amount of people using elevators which are already there will probably factor into how many elevators get installed in the next building. $\endgroup$ – user253751 Oct 10 at 16:24
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    $\begingroup$ Another consideration is that humans have a need for exercise, which they get from stairs but not from elevators. A human should be expending a certain amount of energy just to stay healthy. $\endgroup$ – Dronz Oct 10 at 20:40
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    $\begingroup$ @AlexanderKosubek Buildings need elevators regardless for transporting large objects, people with disabilities, etc. Though I suppose an efficiency analysis for elevators vs hiring some burly men to carry the disabled up the stairs could be interesting. $\endgroup$ – eyeballfrog Oct 10 at 22:13
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"Better for the environment" is not an objective scientific quantity. To do the comparison you need something more specific like "the one that releases the less CO2".

The lift, depending on its type, releases (indirectly) a quite stable amount of CO2 each time someone uses it. It depends on too many factors to know what it is for this specific lift, but considering such a sign was displayed it is probably not a super-clean model.

When you use the stairs your body indeed uses more energy, but this doesn't necessarily means you will eat more: the human body is wasteful and it requires a significant amount of daily effort to reach the level at which you start to eat more. This means that in most cases climbing those stairs will have literally zero effect on environment.

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    $\begingroup$ The human body is not wasteful; it just has a very large energy consumption that doesn't depend on the work you do. And that's a much bigger amount than you consume in any exercise until you get to professional level. It also tends to take a while to learn it needs to eat more; you might not notice a difference the first time you exercise, but after a week, you are eating more. It's not like the body burns extra calories just for fun. But yes, if you really want to reduce your impact on the environment, stop having kids - avoiding the environmental impact of another human trumps all else :D $\endgroup$ – Luaan Oct 11 at 5:39
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    $\begingroup$ The brain uses quite a bit of energy; id you think too much about this issue it will become the dominating pollution factor ;-). $\endgroup$ – Peter - Reinstate Monica Oct 11 at 10:16
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    $\begingroup$ @Luaan it actually is fairly wasteful - muscles are ~20% efficient (Wikipedia). And I'm hardly "professional level" but have been known to burn over 30kJ (7,300 kcal) in a day on a bike. That's ~2.5 days of my typical intake (fairly active). For a day before and several after I'm eating far more than baseline - you certainly do eat extra. $\endgroup$ – Chris H Oct 11 at 11:09
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    $\begingroup$ @ChrisH That was exactly my point. Just being inefficient doesn't mean you eat the same even though you do different amount of work - it just means you need more work to do anything, and thus eat more to do stuff. Anne claims you wouldn't actually eat more. $\endgroup$ – Luaan Oct 11 at 13:44
  • $\begingroup$ @Luaan I'd be interested to know whether there's a threshold level of activity increase that doesn't lead to more consumption - a case in which the answer might be right. (BTW my previous comment was \@ed to you but also aimed to Anne in a way, hence why it's hard to tell whether I'm agreeing with you or not) $\endgroup$ – Chris H Oct 11 at 13:48
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There are two conflicting ways to think about this, both with there own adherents:

  • The work you do is based on renewable energy: food. Even the best elevator uses some electricity, which has environmental impact. Take the stairs!

  • Any building with elevators has air handling, and perhaps air cooling. The heat you add going up stairs takes more energy to extract than what’s needed to run the elevator. Take the lift.

Both of those are over-simplified, which makes the arguments go on and on.

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    $\begingroup$ To carry the argument on and on... Your food energy is only renewable if you grow it in your garden and eat it raw. But what if you eat pineapples flown in from Africa or pulled-pork that's been roasted for six hours? $\endgroup$ – Oscar Bravo Oct 10 at 11:05
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    $\begingroup$ @jeff-y that is from the overall efficiency of the atp reaction which powers the muscles. Quite low compared to electric. $\endgroup$ – Stian Yttervik Oct 10 at 13:37
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    $\begingroup$ ATP is more efficient than a Carnot cycle (no combustion) but even old large-scale electric motors are 90% or more efficient. $\endgroup$ – Bob Jacobsen Oct 10 at 13:56
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    $\begingroup$ @jeff-y that is the production of atp from adp and glucose. Then you need the glucose, which usually the liver makes, although your food contains some. and then you expend the atp to create contraction and adp which is lossy. Then there is the mechanical part, only a fraction of movement is in the direction of travel. It all adds up to a depressingly low figure. To be fair, included should also be the circulatory necessary to transport oxygen and dioxide, but it won't be the biggest contribution. $\endgroup$ – Stian Yttervik Oct 10 at 13:59
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    $\begingroup$ @OscarBravo But unless you've got a really long flight of stairs, energy use for that exercise is negligible compared to your body's static energy requirements. So whether it's renewable or not makes little difference. $\endgroup$ – Graham Oct 10 at 14:33
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I don't think this question can be answered because you need to know a lot of information about efficiency and how electricity is generated and so on (including the efficiency of the generation).

But the big environmental issue with using energy isn't how much heat is generated, it's how much $\mathrm{CO}_2$ is generated. Unfortunately this doesn't really help: the answer can still go both ways I think.

The way that makes the sign perhaps right:

  • you're a vegetarian (better, a vegan), so you are eating plants which have recently captured $\mathrm{CO}_2$ from the atmosphere to make, well, plant, and releasing some of it back into the atmosphere by respiration – this process might even be pulling more $\mathrm{CO}_2$ from the atmosphere than it is releasing into it, I'm not sure;
  • the electricity that powers the lift is generated by fossil fuel, and is therefore turning long-term-stored carbon into $\mathrm{CO}_2$.

The way that makes the sign perhaps wrong:

  • the lift runs from solar power on the roof with perhaps a battery so it works at night;
  • you live entirely off prime beef.
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  • $\begingroup$ BTW, “CO₂” can be perfectly well written with Unicode alone, no MathJax needed. $\endgroup$ – leftaroundabout Oct 10 at 15:32
  • $\begingroup$ @leftaroundabout: yes, I just didn't know how (also, thanks for fixing the missing \mathrms: I should have done that). $\endgroup$ – tfb Oct 10 at 15:33
  • $\begingroup$ I would not write off the heat that easily in favour of the $\mathrm CO_2$. I can see how a major heat and water-steam source influences its surroundings while some claim that carbon dioxide has not that significant role in the Global Warming than it was assumed earlier. $\endgroup$ – Crowley Oct 10 at 21:03
  • $\begingroup$ the electricity generated might be from fossil fuel. or it might be from clean sources like solar, wind, nuclear, etc $\endgroup$ – Phil Oct 11 at 1:39
  • $\begingroup$ @Phil: yes, I mention that in the answer (the example I give is solar power on the roof but I also, obviously, include nuclear &c). $\endgroup$ – tfb Oct 11 at 10:42
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modern lifts use a counterweight that serves as a gravity battery

I believe you've misunderstood that reference. The counterweight isn't there to store energy. It's there to offset the weight of the lift, as well as half the expected load.

This allows the motor operating the lift to, on average, only have to overcome internal friction. Of course, some of the time it has to work a little harder to raise the lift, while other times it has to work a little harder to lower the lift. But in neither case is the counterweight capturing any energy.

If you want to treat the counterweight as a "gravity battery", then logically the lift cab itself must also be a gravity battery. After all, each technically "stores" energy as it's raised, and "releases" the energy as it falls. Note also that taking this stance leads logically to the conclusion that a wheel with its axis oriented horizontally would also necessarily be a gravity battery under this definition. After all, if the wheel is turning, then one side is always losing energy as it descends in the gravity field (giving up "stored" energy), while the other side is gaining energy as it ascends in the same field ("storing" energy).

Personally, I find this way of looking at it unproductive and would not call the counterweight a "gravity battery". In none of those examples is the so-called "battery" storing energy in any constructive manner, because it can only do so by taking that energy from the other "battery" in the system. But judging from some comments, there are at least a couple of people who would disagree. YMMV.

Speaking of internal friction, your analysis seems to leave that out. There is very little friction involved in walking up the stairs, but there's a reasonable amount of friction involved in the systems for a lift, especially a cable-driven one. This friction is just one small part of the overall question of efficiency, which is touched on in other answers.

Suffice to say, those answers are correct to point out that environmentally what will matter is how efficiently energy extracted from the environment is put to work to lift you from one floor to the other. It would not take too much work to show, based on existing research and energy costs, that after efficiency is considered, the typical lift uses way more energy than someone walking does. Biological conversion of energy inputs into energy are generally more efficient at each step — even if one accepts the argument that non-vegetarian diets are less efficient, and we assume a non-vegetarian person — and so of course the overall efficiency is also greater.

All of this doesn't even take into account the additional wear and tear the lift incurs when you use it, which itself will eventually lead to increased impacts on the environment, due to the need to manufacture and replace parts, or even the entire lift itself.

Ironically, the human body is for the most part a "use it or lose it" proposition. While technically walking incurs more wear and tear than standing, it's "built" for that, and the walking actually will help improve the overall reliability and reduce the chances that repair or replacement would be needed (knee surgery, for example). (This is for the average person; for a person with some existing medical issue, the analysis could well be different.)

Finally, one thing not addressed so far is that improving one's own health is itself inherently better for the environment. A person in poor health is going to use energy less efficiently, causing a direct and immediate impact on the environment, and they will also consume greater energy costs as they age, leading to additional impacts. (This assumes, of course, that they live to old age…for better or worse, while people in poor health generally don't live as long, we are good enough at keeping them alive even in poor health that their reduced lifespan does not offset the added impacts that their poor health causes over time.)

I assert that not only is climbing the stairs less impactful on the environment in a direct sense, that when one also takes into account the total environmental impact from beginning to end, it's clear that the disparity is even greater.

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    $\begingroup$ The counterweight captures some energy when the lift goes down and returns it when the lift goes up, so that the motor doesn't have to supply all the energy to move the lift - does that not describe a "gravity battery"? $\endgroup$ – user253751 Oct 11 at 8:19
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    $\begingroup$ +1, "there's a reasonable amount of friction involved" I'd hope so! That's all that stops the heavier of the lift and counterweight plummeting to the bottom! $\endgroup$ – Sam Dean Oct 11 at 14:32
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    $\begingroup$ @immibis: if the counterweight and the lift are in perfect balance, no energy is captured at all. Or, if you prefer: yes, the counterweight captures energy as it's lifted, but that is exactly the same energy that the lift (the other end of the system) is giving up. No net energy is stored, which is the job of a battery. "Capturing" energy isn't useful if that energy is immediately expended somewhere else, and certainly isn't sufficient to justify being called a "battery". You have to store the energy to be a battery. $\endgroup$ – Peter Duniho Oct 11 at 15:16
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    $\begingroup$ This is a physics discussion. Raising the counterweight always stores more potential energy in it. Yes it "gets" that from the cab going down, but that's the whole point. $\endgroup$ – Jeff Y Oct 11 at 15:45
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    $\begingroup$ @JeffY: you are focusing on just one piece of the whole system. That's your prerogative, but in my view it's not useful and I reject the notion that I have to describe the counterweight as a "battery", when doing so means that both the lift and the counterweight would then be a "battery", where one "battery" is always discharging into the other. The "lift" here isn't just the cab, but the whole system, and the whole system as a unit most certainly isn't a "battery". Introducing that term just obfuscates the facts pertinent to the original question. $\endgroup$ – Peter Duniho Oct 11 at 15:48
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The approach that minimizes CO₂ emission is to go to the elevator, wait until some other people go in it in the same direction, and join them. This way you’ll spend less energy, eat less food and emit less CO₂.

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There's another problem with your analysis, which the other answers don't seem to stress enough. You say:

However, gravity is a conservative field. The end result in both cases is that I move up one floor, so the amount of work (i.e. energy) required to get me up one floor is independent of the path I take.

If that were true you could go to the moon and then back to the next floor and you'd use the same amount energy as just going to the next floor. Clearly that's not the case or space travel would have been as cheap as going to the next floor (modulo some air-tight elevator). You simply don't get all your energy back on the return trip (from the moon or the next floor) as usable energy due to the second law of thermodynamics.

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  • $\begingroup$ His comment about the conservative field is true. Your story about going to the moon is full of false logic. Going to the Moon and then down again to the first floor, you do indeed get all the energy back and end up with the same net potential energy as if you'd just walked up the stairs. You've sneaked in a clause about usable energy that is not in the original statement of the Law of Conservation. The Law is only concerned with total energy and does not care whether a human engineer can use it for anything. $\endgroup$ – Oscar Bravo Oct 14 at 6:18
  • $\begingroup$ @OscarBravo: good luck with your type II (or type III) perpetual motion machine then. $\endgroup$ – Fizz Oct 14 at 6:31
  • $\begingroup$ The statement about a gravitational field being conservative is from field theory and it is correct. The change in potential energy between two points in a gravitational field is independent of the path taken. If it weren't, then you could make a Perpetual Motion machine! I think you might be conflating fuel consumption with change in potential - those are not generally equivalent because of inefficiencies in the process. That mixes up field theory and engineering. $\endgroup$ – Oscar Bravo Oct 14 at 14:45
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A modern lifestyle assumed (which can be else there wouldn’t be the elevator nor the note) and a person which didn’t have already enough movement (since you agree with the health benefit, I guess you do too), indeed both are true:
Since for health some movement is good anyway, one doesn’t have to consider the calories burned, else the calories may just end up as (possibly unhealthy) fat. One could also consider someone doing some exercising in the office after having taking the elevator, so the energy for the elevator is saved for those walking instead of exercising.

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Ok enough with all this theory and philosophy. I had exactly the same question and decided to answer it empirically!

TLDR;

If the elevator is going up anyway, then you should hop on since your additional weight has almost no effect on the total power used.

If you are considering taking the elevator alone, you should take the stairs.

Note that this advice is based solely on the single hydraulic piston elevator that I tested and may not necessarily apply to all elevators, but interesting findings nonetheless!

Full explanation and data here:

https://wp.josh.com/2013/05/29/elevator-power-usage-should-i-take-the-stairs/

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  • $\begingroup$ You should summarize more of the link information in your post. For example, it's very important to note that you tested this on a hydraulic lift elevator, not a traction elevator, which does operate with different efficiency. Traction elevators are considered the more common traditional type. $\endgroup$ – JMac Oct 16 at 2:22
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There may in fact be a physics answer to this question, but this is a sociological question on other levels.

Taking the stairs when an elevator is available is a behavior with an intent behind it.

If the intent to "be good for the environment" is abandoned because of uncertainty about the magnitude of your act's effectiveness, there's no possibility at all that it can succeed.

Behaviors like this are examples of "thinking globally and acting locally". What's probably (in this case) even more important than the specific amount of energy conserved is the demonstration of your human motivation to try. If you don't set an example, there's no chance that others will follow it. We're not acting alone.

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