Escalators and potential speed

There was a very old radio program on I think X minus one…called Let the Roads

roll. Idea was in the future, there would be no cars as such. Just continually accelerating escalators which could reach tremendous speeds, given time. Nobody drove. Just kept walking on escalators at ever increasing speed.

That idea has always fascinated me. I would like to know how long it would take for a man to reach 100 miles an hour if the escalator he was riding accelerated say 2 miles an hour every ten feet and the man was walking at 2 miles hour. (Hardly strenuous and the acceleration would be unnoticeable to the man).

Assuming no wind resistance (maybe big fans and an enclosed tunnel with the fans neutralizing any wind factor.)

How long would it take to reach 1000 mph? 10,000 miles per hour? 100,000 mph?

I am very bad at math. So a asking for some help here.

The story is by Heinlein, and is titled “The Roads Must Roll.”

Asimov has a similar system in his Elijah Baley novel “The Caves of Steel.”

In The Roads Must Roll, they actually accelerated the people by having multiple strips running in parallel, each one a good quick step faster than the other, so you’d just hop from one to the other in order to speed up or slow down. Most of your time in doing so would involve traversing the strip, which would be wide enough to accommodate small shops & restaurants. The roads themselves were wide, fully-enclosed buildings running from city to city and scarred the landscape for generations to come.

Having one of the strips break was… not a good thing.

Sorry for the wrong title.

But the escalator wouldn’t really have to be parallel to work. Just straight forward with 2mph increasing speed…say every 10 feet. Seems like it would be like a normal walk. You just keep going faster and faster without really noticing anything unusual.

Still curious about how long it would take to reach astonishing speed.

Acceleration is expressed as (a unit of distance) / (a unit of time)[sup]2[/sup]

If you express it as distance / time / distance, I’m not sure how it’s going to go. You start at 0 m/h and the time it takes you to travel 10 feet is – um…

Ok, let’s start at 2 m/h. The time to travel 10 f is 10f/(2m/h) = 10f/(5280f/m x 2m/h) = 10 f / (10560 f/h) = 0.000947 h or about 3.41 seconds. Your average acceleration is 2 m/h / 0.000947 h = 2112 m/h[sup]2[/sup]

But that’s not right because because we were accelerating all that time and the calculation I did assumed 2 m/h steady. I’m probably past the age where I can learn how to deal with varying rates of acceleration although there are some on the dope who can handle it.

The problem would be very simple if you ask for a constant rate of acceleration in some number of miles/hour[sup]2[/sup] or miles / hour / hour if you prefer – as in 4 mile / hour faster every hour.

It is more of a math question than anything else. And that’s what I am not very good at.

So what speed would you attain if your speed was increased by an escalator by 2mph every 10 feet and you are walking at 2 mph …over time.

Say over 24 hours.

Say it takes 2 seconds to go ten feet

Just a guess…about 2 seconds, .but probably pretty close.

Probably pretty simple to figure out for anyone good at math. But that’s not me.

If his speed is increasing by 2 mph for each 10 ft he travels, he’s got problems - because the time it takes to travel that distance steadily decreases. His acceleration thus steadily increases, and before long will be severe.

For example, by the time he’s traveled 2000 ft, he’s doing 400 mph. At that speed, he covers 10 ft in about .017 seconds, and his acceleration is around 5.4G - probably the onset of blackout for many.

A mile from the start, he’s reached an acceleration that will kill most humans.

I’m not sure that black out would be a problem assuming gigantic fans keep pace with the speed …Seems like everything would be normal for the man walking. Just like riding in a car or on an airplane.

And isn’t acceleration relative.? To where you are?

You are probably right. Just trying to learn.

Wow… 400 mph in 2000 feet.

Just curious and allowing for fatal blackout…After 24 hours…How fast would the probably dead man be going?

Acceleration isn’t relative, and fans wouldn’t help. The problem isn’t that the guy’s going to fall over from the wind, it’s that his internal organs are going to be crushed into chunky salsa.

If you wanted to actually make such a system, though, it’d be simple enough: Just make the faster segments longer, so it’s a fixed amount of time between speed-ups instead of a fixed amount of distance.

Do you mean “the velocity of the escalator increased by 2 mph over 10 feet”? If so, that works out to be somewhat easy.

If you mean the acceleration increased by 2 miles per [some unit time]^2, every 10 feet, then yes…probably death soon. :wink:

What you want is to accelerate at 1g over a distance…

http://www.madsci.org/posts/archives/2000-05/959372903.Ph.r.html

Yes, I did mean the velocity of the escalator would increase by 2 mph every ten feet…to exactly match the walking speed of the man. So he would notice very little of any change every 10 feet but would keep going faster and faster.

Wait, point of clarification: Do you want each segment of escalator to be 10 feet long, or do you want the walker to reach a segment boundary every time he walks 10 feet relative to his current surface? The former will lead to crushingly large accelerations, but the latter won’t.

IIRC according to the story (and the X Minus One episode-- kudos on listening to those!), the escalator didn’t work that way.

There were several parallel tracks. The outside-most track moved, for example, 5 MPH. The next one moved 10 MPH, the next 15 MPH, etc, until the furthest track was something like 100 MPH (I don’t remember the actual speed). So to “accelerate” you get on the slowest track and then step left to the faster track, keep stepping left until you’re going the speed you want. To get off, you just do the reverse and step off the slowest track.

The system was constructed so that these escalators could handle people and cargo and basically networked the entire country like the freeway system does now, and the plot was about a labor strike causing the escalators to be sabotaged and lurch to a sudden stop. This of course causes chaos, because the society was entirely dependent on the escalator system.

Both sound about the same to me.

I want each segment of escalator to be 10 feet long with each segment moving 2 mph faster than the last one. Thus enabling the walker to reach 2 mph before reaching each segment and feel almost no sense of change encountering each segment. He would be steadily increasing speed without noticing.

Sounds more like your second option, since I think it would take quite a while that way to achieve great speed. Just not sure how long it would take to reach 100 mph or 10000 mph that way.

It also seems that the walker would feel no acceleration…all he would feel would be the 2 mph on accelerating he was doing himself…from a virtual standstill at the beginning of each segment to the 2mph he reaches before the next segment.

And the segment could be longer than 10 feet. Just guessing it would take about 10 feet for someone to go from a standstill to 2 mph.

For the walker I think it would seem like he was starting from a standstill and increasing his own speed to 2 mph over and over again.

Don’t see how he would feel any acceleration except his own.

If each segment is 10 ft long and moves 2 mph faster than the previous segment, you do end up with some very fast acceleration. The issue is that those 10ft segments take less and less time as you progress. See below:

1st 10 ft: 3.4 seconds
2nd 10 ft: 1.7 seconds
3rd 10 ft: 1.14 seconds
4th 10 ft: 0.85 seconds

and this continues until, by the time you’ve gotten to the 10th 10 ft section, you have 0.34 seconds to step off onto the next segment. You’ve also accelerated from 0 to 20 mph in just 9.99 seconds. At this point, your total acceleration may not be that bad, however, your ability to jump from segment to segment is starting to get challenged.

Now, because acceleration is tied to the 10ft segments, you keep accelerating faster. So while it only took you 10 seconds to get to 20 mph, in just 5 more seconds (15.34), you’re already doing 100 mph. At that speed, you’ve got roughly 0.07 seconds between segments, so you’d better be light on your toes. Of course, there’s no time to think about that, because in just 8 more seconds (23.16 total) you’ll be doing 1,000 mph.

The problem with your situation is that you’re assuming the segments should all be the same length. Instead, the segments should be designed that the walker spends the same amount of TIME on each segment. So as you go to faster and faster ones, they’d have to get progressively longer.

For example, let’s assume they are all 10 ft. When he’s walking 2mph, he’d go 10 feet in about 3.4 seconds. When he’s walking on the ramp going 2mph, he’d go 10 feet in 1.7 seconds. When he’s on the next ramp, he’d go 10 feet in 1.13 seconds. At this point he’s only going 6mph, but already the ramps are so short that he probably doesn’t have enough time to take a step before he hits the next ramp. Pretty soon he’s going to hit a ramp and just fall.

So let’s assume that the belts are designed with increasing lengths so that he always spends 2 seconds on each.

The speed he would be moving in mph would be equal (2 + t), where t is the number of seconds that has been walking - after 2 seconds, he’d be at (2+2) = 4mph; after 60 seconds, he’d be at (60+2)=62mph.

However, the length of each belt would be:

length = 2.933 * (t)

So the “60mph belt” would have to be 176 feet long. The total length required to get up to 60mph would be 2728 feet, or nearly half a mile. Assuming the same amount of length to decelerate, you would take about 2 minutes to cover a mile, or averaging about 30mph.

If you wanted to get up to 120mph, the individual track section would be twice as long (352 ft), but total length would be four times as much (10736 ft).

But one big problem is, no matter how slowly you accelerate, the “seam” between sections is still stationary. So if you’re moving at 60mph, that gap between belts will approach you at 60mph. You’d have to have really quick reflexes to be able to step over it. Just imagine being on an escalator at the mall, and having it moving at 60mph. Ignoring the quick deceleration when you step off, you still will have a lot of trouble stepping off at just the right time.

First off - dammit, an escalator goes up or down! What we’re talking about here are moving sidewalks, a different (but related) concept! :wink:

Secondly, with all this talk of a single moving sidewalk (slidewalk?) that accelerates after you’ve been on it for a while… just how do you get off? Is it a path to a single fixed terminus that will take you back down to a safe exit velocity when you get there? Because otherwise you’d get the problem of pedestrians having to board and deboard while the slide is at high speeds.