When you run up an escalator, is that more steps or fewer?
June 4, 2018 3:02 PM Subscribe
Say you have a really long escalator, like inside many subway stations. If you run up the steps, are you stepping on fewer steps than you do if you walk up at a fast pace? At a normal pace? Or is it the same number of steps because you're still traveling the same distance, which requires a certain number of steps to reach? Or fewer steps because you're going faster than the rate of speed of the escalator itself? Assume you're not skipping any steps on your way up.
I'm not an escalator expert by any means, but I think that the faster you go, the more steps you end up going on.
I came to this conclusion by thinking in the opposite: If you go as slow as possible (i.e. not moving), you would go up zero steps. If you go really slow, you might go up 2 or 3 steps by the time the escalator reaches the top. So on until you're going as fast as possible.
posted by hydra77 at 3:07 PM on June 4, 2018 [2 favorites]
I came to this conclusion by thinking in the opposite: If you go as slow as possible (i.e. not moving), you would go up zero steps. If you go really slow, you might go up 2 or 3 steps by the time the escalator reaches the top. So on until you're going as fast as possible.
posted by hydra77 at 3:07 PM on June 4, 2018 [2 favorites]
The faster you go, the more steps you'll take.
If the escalator has 100 steps, the range of number of steps based on speed goes from zero (standing on the escalator, not taking a step from beginning to end) to 100 (sprinting up and catching every step before the escalator completes one step-advancement).
edit: jinx!
posted by blueberrypuffin at 3:07 PM on June 4, 2018
If the escalator has 100 steps, the range of number of steps based on speed goes from zero (standing on the escalator, not taking a step from beginning to end) to 100 (sprinting up and catching every step before the escalator completes one step-advancement).
edit: jinx!
posted by blueberrypuffin at 3:07 PM on June 4, 2018
I don't have a definitive answer, but just to further illustrate the problem here: if you stand completely still on the escalator, you effectively climb zero steps because the escalator is doing the work for you. If you run or walk up, you obviously take some steps.
I'd guess you're probably right that the faster you move, the more steps you actually climb, but it'd be interesting to see the math.
posted by LionIndex at 3:09 PM on June 4, 2018
I'd guess you're probably right that the faster you move, the more steps you actually climb, but it'd be interesting to see the math.
posted by LionIndex at 3:09 PM on June 4, 2018
If you take consistently sized steps, at a similar pace you would get to your destination faster on the escalator by taking fewer steps than if you had taken the stairs.
Say the vertical distance you have to climb is 100 feet, and each step is 2 feet vertically (for easy math). on the escalator you would need to take substantially fewer than 50 steps to reach the top because youre rising the entire time, whether youre stepping or not.
posted by Exceptional_Hubris at 3:10 PM on June 4, 2018
Say the vertical distance you have to climb is 100 feet, and each step is 2 feet vertically (for easy math). on the escalator you would need to take substantially fewer than 50 steps to reach the top because youre rising the entire time, whether youre stepping or not.
posted by Exceptional_Hubris at 3:10 PM on June 4, 2018
I guess the other assumption is that you're running up an up escalator, not a down one?
posted by Kurichina at 3:26 PM on June 4, 2018 [4 favorites]
posted by Kurichina at 3:26 PM on June 4, 2018 [4 favorites]
For a (hopefully) different way of looking at this, if you have to touch every step (ie not doing every other by running) then the faster you move, the more steps you have to climb. Imagine the very split second you get on the escalator - there are (say) 60 steps between you and the top. The slower you go, the more steps 'disappear' between you and your end point, because the escalator itself is rising. So the escalator is doing some of the work for you (by removing steps from the top bit) so the less time you give it to do that, the more work you have to do yourself. Stationary stair case? You walk all 60 steps. Massively fast elevator? You don't walk any steps. It's a sliding scale between.
So if we put the escalator to a sane speed and say those 60 steps disappear at 1 step per second, then if you can run up the escalator in 20 seconds, only 20 steps have disappeared (between you and the end point) by the time you get to the top - you had to walk the remaining 40 yourself. If you walk up at half that speed, then in the 40 seconds it took you, 40 have disappeared, you only have to walk the remaining 20. Make sense?
posted by Brockles at 3:31 PM on June 4, 2018 [2 favorites]
So if we put the escalator to a sane speed and say those 60 steps disappear at 1 step per second, then if you can run up the escalator in 20 seconds, only 20 steps have disappeared (between you and the end point) by the time you get to the top - you had to walk the remaining 40 yourself. If you walk up at half that speed, then in the 40 seconds it took you, 40 have disappeared, you only have to walk the remaining 20. Make sense?
posted by Brockles at 3:31 PM on June 4, 2018 [2 favorites]
Other people have already given the right answer, but I wanted to emphasize the procedure for getting it, since it's useful in so many contexts:
- First, realize that either the number of steps you step on keeps going up as you go faster, or keeps going down. It's not going to change direction in the middle, because that wouldn't make any sense.
- Then, think about the extreme cases of walking reeeeeallly slowly or walking reeeeeallly fast.
- Now you know what direction the relationship takes in between!
This method of considering extreme cases to get an immediate sense of the behavior of the whole system is one that scientists and mathematicians use all the time (seriously, daily), but as you see here it doesn't actually require any calculation at all so it's something anyone can learn to do.
posted by dfan at 3:37 PM on June 4, 2018 [18 favorites]
- First, realize that either the number of steps you step on keeps going up as you go faster, or keeps going down. It's not going to change direction in the middle, because that wouldn't make any sense.
- Then, think about the extreme cases of walking reeeeeallly slowly or walking reeeeeallly fast.
- Now you know what direction the relationship takes in between!
This method of considering extreme cases to get an immediate sense of the behavior of the whole system is one that scientists and mathematicians use all the time (seriously, daily), but as you see here it doesn't actually require any calculation at all so it's something anyone can learn to do.
posted by dfan at 3:37 PM on June 4, 2018 [18 favorites]
However, there is an upward bound to the number of steps. So if you went infinitely fast, there would not be an infinite number of steps. The maximum number of steps is how many there would be if the escalator was stopped and you had to go up it like a regular set of fixed stairs.
posted by metahawk at 4:47 PM on June 4, 2018 [1 favorite]
posted by metahawk at 4:47 PM on June 4, 2018 [1 favorite]
Best answer: I think what you are really asking here is which is the fastest/most efficient approach to take, but that is almost unanswerable because it depends on many factors - how long the steps are, how fit you are and what the rest of the journey is like.
Lets assume the escalator is 50 steps long and when you reach the top it leads to another fixed staircase which is also 50 steps long.
If the escalator travels at 1 step/sec it will take 50 seconds if you stand still.
Running you can maybe half that time, so lets say 25 seconds.
Now on the fixed staircase lets assume it takes twice the time, so 100 seconds to walk and 50 seconds to run.
So if you stand on the escalator and run on the stairs - total time is 50 standing+50 running = 100 seconds.
If you run on the escalator and walk the stairs - total time is 25 run+100 walk = 125 seconds.
It is 25% faster to run on the stairs, BUT that means you have to spend twice as long running.
if you stand on the escalator and run on the stairs but only for the first 25 seconds, that will get you halfway up the staircase so the total time becomes 50 standing+25 run+50 walk = 125 the same time as running on the escalator but you halved the walking time.
So on these numbers, if you have the energy to run for 25 seconds it is better to do it on the stairs than on the escalator.
posted by Lanark at 4:49 PM on June 4, 2018
Lets assume the escalator is 50 steps long and when you reach the top it leads to another fixed staircase which is also 50 steps long.
If the escalator travels at 1 step/sec it will take 50 seconds if you stand still.
Running you can maybe half that time, so lets say 25 seconds.
Now on the fixed staircase lets assume it takes twice the time, so 100 seconds to walk and 50 seconds to run.
So if you stand on the escalator and run on the stairs - total time is 50 standing+50 running = 100 seconds.
If you run on the escalator and walk the stairs - total time is 25 run+100 walk = 125 seconds.
It is 25% faster to run on the stairs, BUT that means you have to spend twice as long running.
if you stand on the escalator and run on the stairs but only for the first 25 seconds, that will get you halfway up the staircase so the total time becomes 50 standing+25 run+50 walk = 125 the same time as running on the escalator but you halved the walking time.
So on these numbers, if you have the energy to run for 25 seconds it is better to do it on the stairs than on the escalator.
posted by Lanark at 4:49 PM on June 4, 2018
Supercres is correct. If you are running up a DOWN escalator though, it would be the other way around.
posted by w0mbat at 6:19 PM on June 4, 2018
posted by w0mbat at 6:19 PM on June 4, 2018
If you are running up a DOWN escalator though, it would be the other way around.
No. It works the same either way. I can't see why you think you'd use less steps if you ran quickly down an escalator than if you stood there and used one.
posted by deadwax at 5:24 AM on June 5, 2018
No. It works the same either way. I can't see why you think you'd use less steps if you ran quickly down an escalator than if you stood there and used one.
posted by deadwax at 5:24 AM on June 5, 2018
The equation I get is:
# of stairs you climb = KVr / (Ve + Vr)
where K is the number of stairs on the escalator
Ve is the velocity of the escalator
Vr is the velocity you're running.
When you're not running (Vr = 0), you climb 0 stairs.
When you're running exactly as fast as the escalator (Vr = Ve), you climb half the stairs (K/2).
It's irrelevant whether you're running up an up escalator or down a down escalator.
The equation should still work if you're running up a down escalator or down an up escalator -- but it blows up if you're running as fast as or faster than the escalator (Vr >= -Ve), which makes sense, as you'll never get to the finish line.
posted by cgs06 at 6:09 AM on June 5, 2018 [2 favorites]
# of stairs you climb = KVr / (Ve + Vr)
where K is the number of stairs on the escalator
Ve is the velocity of the escalator
Vr is the velocity you're running.
When you're not running (Vr = 0), you climb 0 stairs.
When you're running exactly as fast as the escalator (Vr = Ve), you climb half the stairs (K/2).
It's irrelevant whether you're running up an up escalator or down a down escalator.
The equation should still work if you're running up a down escalator or down an up escalator -- but it blows up if you're running as fast as or faster than the escalator (Vr >= -Ve), which makes sense, as you'll never get to the finish line.
posted by cgs06 at 6:09 AM on June 5, 2018 [2 favorites]
No. It works the same either way.
No, they're right. They are talking about running opposite to the direction of the escalator. So what they are saying in that context is correct, I just have no idea why it came up in this question.
posted by Brockles at 7:27 AM on June 5, 2018 [2 favorites]
No, they're right. They are talking about running opposite to the direction of the escalator. So what they are saying in that context is correct, I just have no idea why it came up in this question.
posted by Brockles at 7:27 AM on June 5, 2018 [2 favorites]
The answer is indeterminate at stated. We need to know if you're stepping with or against the direction of the escalator's steps. Though you did state "faster than the rate of speed" which could be interpreted as stepping with. I'm not convinced "rate of speed" implies a direction, though I could be wrong.
posted by Pig Tail Orchestra at 9:40 AM on June 5, 2018 [1 favorite]
posted by Pig Tail Orchestra at 9:40 AM on June 5, 2018 [1 favorite]
As Pig Tail Orchestra comfirms, the problem states you are running up, but not whether it is an UP or DOWN escalator, so I solved both cases in my head. They are not the same.
With the case of running against the flow, running speeds lower than the escalator speed will never complete the task and give a result of infinity, a speed very slightly above the escalator speed will give a huge step count which depends on how small the margin is, and running at infinite speed touches only the number of steps visible.
posted by w0mbat at 11:42 AM on June 6, 2018
With the case of running against the flow, running speeds lower than the escalator speed will never complete the task and give a result of infinity, a speed very slightly above the escalator speed will give a huge step count which depends on how small the margin is, and running at infinite speed touches only the number of steps visible.
posted by w0mbat at 11:42 AM on June 6, 2018
Lets assume the escalator is 50 steps long and when you reach the top it leads to another fixed staircase which is also 50 steps long.The intuitive explanation for this is that you want to maximize the amount of time during your trip that the escalator is doing work for you for free.
[...]
So on these numbers, if you have the energy to run for 25 seconds it is better to do it on the stairs than on the escalator.
posted by dfan at 8:19 AM on June 8, 2018
Response by poster: Okay. I figured out why this question was bugging me - and thanks to Lanark for figuring it out before I did -- I was asking the wrong thing.
I guess my real question should have been, When you have a 2-3 story stairway, and the choice of stairs or an escalator to go up, is it more stairs to run vs. walk compared to taking the stairs?
posted by Mchelly at 7:12 AM on June 21, 2018
I guess my real question should have been, When you have a 2-3 story stairway, and the choice of stairs or an escalator to go up, is it more stairs to run vs. walk compared to taking the stairs?
posted by Mchelly at 7:12 AM on June 21, 2018
Seeing the question rephrased, I'm not sure anyone has actually answered it. The slower you go on the escalator, the less stairs you will use. So assuming the step count for both stairs and escalator are the same, the answer is yes, it is more stairs to run vs. walk compared to taking the stairs. But really, this is literally the purpose of escalators: to use less stairs.
posted by Pig Tail Orchestra at 9:16 AM on June 26, 2018 [1 favorite]
posted by Pig Tail Orchestra at 9:16 AM on June 26, 2018 [1 favorite]
This thread is closed to new comments.
If you ride the escalator and don’t walk at all, you use one step.
If you “walk” so slowly that in the entire trip you climb a single step, you use two total steps.
If, however, you run so quickly that the motion of the elevator is negligible compared to you, you use all the steps, as if you were going up normal stairs.
The faster you go, the more steps you hit.
posted by supercres at 3:07 PM on June 4, 2018 [32 favorites]