Where does this figure come from? Sorry for being dense.
In “The City and the Stars”, Clarke posited a solid surfaced roadway which was fixed at both ends, but ran at increasing speeds in between. Very cool.
That appears to be the value for acceleration multiplied by (t) time.
2 miles/hour = 2.933 ft/sec
Since in this example “t” is equal to both the time and your current speed, 2.933(t) is the distance traversed at your current velocity.
Another wait a minute wait a minute “the man was walking at 2 miles hour”
Why is the man walking at all - he’s on an accelerating moving sidewalk. math is the least of your problems.
Simple Grade 10 physics formulas:
d= 1/2(at^2) d- distance in feet, a- acceleration in ft/sec^2 t- time sec.
v=at v-velocity
v^2=2ad
For comparison, G=32 ft/sec^2, and 88ft/sec=60mph, so 100mph=146.7ft/sec
2mph = 2.93ft/sec, so let’s round to 3ft/sec
Thus: for 100mph or 146.7ft/sec :
accelerate 2mph every 10 feet -
2^2=a(10)
a=4/10=0.4ft/sec^2 is your acceleration. Not fast.
How long to 100mph (146.7ft/sec?)
v=at so: 146.7= 0.4t
t=(146.7/0.4)= 366.7 seconds - just over 6 minutes.
v^2=2ad so d=(146.7^2)/(2)(3)=3587 feet - well over half a mile.
Of course, the question is poorly worded - I assume increase of 2mph the first 10 feet defines the constant acceleration. By the time you’re going 66mph, adding another 2mph in 10 feet is pretty good acceleration -almost18mph each second. I assume you mean constant acceleration from the point of view of the guy on the escalator.
Great math input here.
So what most of you are saying is that the scientific basis for “The Roads Must Roll” is fallacious. Would never work practically.
Of course in the original X Minus One the moving roads did run parallel to each other at ever increasing speeds as has been pointed out.
I assume the math is still the same for that and it just flat out wouldn’t work even to reach speed of say 100 mph as in the original radio play.
If the belts were moving parallel to each other, it would work fine. The guy would just need to hop to the next belt, take a moment to stabilize himself, then hop to the next one, etc. The acceleration would be time-based and would depend on how quickly he hopped to the next belt.
This is opposed to inline belts that are ten feet long where you’d be spending less and less time on each belt. This might work out well the first few belts but when you’re trucking at about 500 MPH, you’re going to cross each belt in the blink of an eye and hit the next that’s going 2 MPH faster. It’s just not possible. You’d either have to make the belts incrementally longer or make the change in speed incrementally lower to maintain the same average acceleration.
What would happen if a plane tried to take off of one of these things?
Ok.
Guess I should have stuck with the original parallel belts. Was easier for me to imagine the transition in speed going straight ahead and didn’t think it made any difference whether going straight ahead of or off to the side. But it does.
So back to the original question this time jumping to the side on a faster belt.
Say still 2 mph faster for each belt. (The original radio play had increments of speed increase at 5 mph…but that would be like a run to match the 5 mph of the next belt. I like 2 mph better because it would be more of a leisurely stroll and not a work out which would get exhausting after a few hours.
So using parallel roads and 2 mph increases in speed…How long would it take to reach 100 mph? 1000 mph? 100000 mph?
And I had an entirely different interpretation of the OP. I imagined the 10 feet being perpendicular to motion of the sidewalk i.e. walking across it so the only acceleration is when they change to another sidewalk.
I just realized that I’ve asked for an answer in time without being specific enough.
Still the same. Parallel belts maybe 2 feet wide. Walker would still take 10 seconds to get his speed up to 2 mph to match the 2 mph greater speed of the next belt, and then just step over to the left. There might be a balance problem when stepping over…but I think the body would just get used to that with a little practice.
Just want to add info for unleisurely New York walkers, who will need different moving platforms, once you guys work out the physics.
Uptown-downtown blocks in Manhattan–eg, 14th-15th street–are 20 to a mile. It takes about a minute to walk one of these blocks. Hence you know distance and walking time, for a New York stride.
I always find it amazing that most New Yorkers don’t know this, or that it is not standard info in tourist guide books.
Carry on.
That is different from the original radio play…but I guess perpendicular would work too. It might be more of a balance problem than the parallel way…but maybe your body would just get used to that too with practice.
I’m picturing walking perpendicular to the track to get to the edge of the slower belt, turning 90 degrees to face in the direction of motion then moving to the faster belt. 2 mph is just under 3 ft/sec so while it may take practice it is not undoable.
Simply divide the speed you’re trying to reach (and technically you should subtract 2 MPH from that since that’s your starting speed, but that isn’t significant) by the speed difference between belts and then multiply that by the number of seconds he spends on each belt. Thus to get to 100 MPH with your values would take 500 seconds, or 8 minutes 20 seconds; 1000 MPH would take 5000 seconds, etc.
Haven’t read Heinlein’s “Roads Must Roll” for over 40 years. IIRC, there were a series of parallel belts, as mentioned, each going faster. During the strike the side belts were shut off stranding people on the 100mph belt. Or was it the middle was turned off and the side belts whizzed by at 95mph? I assume the belts actually swing in a wide circle and return the other way, so there is no brick wall at the end…
I think Snailboy has it best.
If you are spending 10 sec on each belt, and each is 2mph faster, then for 100mph there are 50 belts and you are going to spend 10x50=500 seconds getting up to speed.
Assuming 2mph is about 3 fps (actually, 2.93)
Each belt is going 3n fps faste; distance travelled on a belt is 10sec x 3n Ft/sec
Sum n from 0 to 50 of: (10)x(3n) = 38250 - over 7 miles.
(plus whatever distance you walked in 500 seconds - maybe an extra half-mile?)
I did this on a spreadsheet, the easiest way. it’s been a while since I did series stuff.
This is a long distance because 10 seconds at each speed is actually a very long time.
I never could visualize what was going on in The Roads Must Roll. The top speed was fairly high; was it 150 mph? Assuming that you have a differential of 2 mph between belts, that would mean that you would have to cross 75 belts to get to top speed, and then cross 75 belts again to get off. That would be difficult and time-consuming and take up a lot of space.
But a bigger problem is that Heinlein obviously contemplated structures on the belts. What happens to these? You can’t just have a belt that turns upside down. How do the belts turn around?