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Some Saudi prince has proposed a 100 mile long city, a 5 minute walk wide. This is stupid but I was more sympathetic than others, until I did math. Pasting a comment:
But I've convinced myself even a reasonable version is stupid, using math.
Imagine a sensible linear city, 10 miles long, 1 wide. east-west, say.
Now we could make it 10x longer, 100 miles long. Would take forever to get from end to end but hopefully that doesn't happen often. Big advantage: it's a short walk to get to not-city, wherever you are.
Or we could put 9 more cities side by side, making a square. 100 miles of track in 10 10-mile lines... but to keep connectivity, we'll need as much again north-south, so 200 miles of track. So there's your doubling of infrastructure.
OTOH with the Line your longest trip is 100 miles; with the Square, it's 20 miles, from corner to corner. And from the Square center you can reach any point in 10 miles, while from the Line center you can reach only 20% in a 10 mile trip.
If we compare a 1000 mile long Line to a 33x33 mile grid (LA! if LA were sensible), the infrastructure still only doubles, but now the Line trips reach only 1/16th of what the Square trips do. OTOH from the center it's a 16 mile train ride to get outside the city, instead of a 10 minute walk.
So for city access the grid is a pretty solid win, the more so the bigger you get.
OTOH going smaller, 10 mile Line vs. 3.3x3.3... longest trip is 10 miles vs. 6.6 miles; 3.3 mile trip on the Line gets you 2/3 of the city. A grid doubles your infrastructure while getting you only 50% more coverage. This might be why I remembered lines winning, I'd previously modeled this at a small scale.
So if you're ever some idealized city planner, it may make sense to think in terms of mile-wide strips, rather than a grid expanding in two directions. But between 5 and 10 miles of length you'll want to start laying down more strips, rather than simply extending.
But I've convinced myself even a reasonable version is stupid, using math.
Imagine a sensible linear city, 10 miles long, 1 wide. east-west, say.
Now we could make it 10x longer, 100 miles long. Would take forever to get from end to end but hopefully that doesn't happen often. Big advantage: it's a short walk to get to not-city, wherever you are.
Or we could put 9 more cities side by side, making a square. 100 miles of track in 10 10-mile lines... but to keep connectivity, we'll need as much again north-south, so 200 miles of track. So there's your doubling of infrastructure.
OTOH with the Line your longest trip is 100 miles; with the Square, it's 20 miles, from corner to corner. And from the Square center you can reach any point in 10 miles, while from the Line center you can reach only 20% in a 10 mile trip.
If we compare a 1000 mile long Line to a 33x33 mile grid (LA! if LA were sensible), the infrastructure still only doubles, but now the Line trips reach only 1/16th of what the Square trips do. OTOH from the center it's a 16 mile train ride to get outside the city, instead of a 10 minute walk.
So for city access the grid is a pretty solid win, the more so the bigger you get.
OTOH going smaller, 10 mile Line vs. 3.3x3.3... longest trip is 10 miles vs. 6.6 miles; 3.3 mile trip on the Line gets you 2/3 of the city. A grid doubles your infrastructure while getting you only 50% more coverage. This might be why I remembered lines winning, I'd previously modeled this at a small scale.
So if you're ever some idealized city planner, it may make sense to think in terms of mile-wide strips, rather than a grid expanding in two directions. But between 5 and 10 miles of length you'll want to start laying down more strips, rather than simply extending.
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Date: 2021-01-23 06:55 (UTC)From:Thus the advantage of the long city 5 mins wide is that you can service the entire thing with a single *really good* train line? (I'd do two in parallel actually, one going at much higher speeds for the longer ranges, or have buses for the short-range anyway even though you only have one bus route).
This opens up *so* much optimization-space that you couldn't do otherwise, I bet. Though probably you might have trouble getting the bandwidth you need if you weren't stupid you'd be commiting a lot of money from the get-go to making sure you were.