I'd guess that Heinlein was aware of it and scaled it up in his imagination.
  The Roads must roll — they are the arteries of the nation. When they stop, everything stops. Factories idle, food rots, men starve. The nation cannot live without its Roads.
  
  A thousand feet wide, level as a floor, strip after strip moving past in ordered procession. The slow strips on the outside moved at five miles an hour; the inner ones faster and faster, until the express strip in the center rushed past at a hundred miles an hour.
  -- The Roads Must Roll, Astounding Science Fiction, June 1940.
https://ia601208.us.archive.org/32/items/calibre_library_178...I read this as a teenager in a Sci-Fi compilation without paying much attention to the author, so I forgot where I read it or who wrote it or where I could find it again. But I composed and tape-recorded a melody to the lyrics which still hums in my head :
  While you ride
  While you glide
  We are watching down inside
  that your roadways go rolling along. ...
Thanks for posting.Also Arthur C Clarke in The City and the Stars (1956):
“An engineer of the ancient world would have gone slowly mad trying to understand how an apparently solid roadway could be fixed at the sides while toward the centre it moved at a steadily increasing velocity.”
This somehow feels like the horizontal equivalent of a Pater Noster elevator. But probably with even worse error modes if it stops working at 100mph.
I think about this every time I get on a moving walkway and wish it had a few more speeds.
Yeah, love that idea of progressive velocities. I ant someone to at least build a short test track like this so we can play with it.
Seem to recall they were called "slidewalks" by some Sci-Fi author—probably Heinlein, eh?
They have an inner and outer set of moving sidewalks as the loading area for one of the Harry Potter Universal Orlando rides (the one in Hogwart's Castle.) It's extremely disorienting at first but they have lots of staff moving people into the seats, so no one ends up hitting the walls.
We were casually waiting in line for a while, then suddenly we were led into the area to get onto the ride and had a 'holy shit, they're serious about this one' moment.
Edit: the Universal Hollywood ride doesn't seem to have this (as of 2024), so I'm not sure if the Orlando one still does.
The slow strips on the outside moved at five miles an hour; the inner ones faster and faster...
Not good enough. The same strip should go faster and faster over time and decelerate near its end. It sounds impossible, but I can think of a few ways to make it work.
It was a recurring theme throughout most of Golden Age fiction.
E.g. Clifford D. Simak mentions them as a mode of transportation in The Goblin Reservation, Asimov has them in Robots of Dawn, and I'm sure I'm forgetting plenty more.
It could be that it was Heinlein who kicked of the trend.
Wow, this is exactly the staggered-speed walkway system I once saw in a Philip K. Dick short story, forget which, but obviously it was written after this.
Asimov went into some detail with this premise too, in Caves of Steel iirc. I suppose he probably got it from Heinlein.