## Saturday, May 23, 2015

### Calculations on urban sprawl

Here is another article about urban sprawl.  It describes a recent study done that indicates that urban sprawl costs US society some \$1trillion annually, mainly in unproductive driving time and externalities like pollution.

The author of the study makes the modest recommendation that we in the US should aim for metro area residents to live at a density of 10 people or 5 households per acre.  This seemed remarkably low to me, but I was surprised that this was the top fifth of urban density in the US, meaning that the vast majority of metro area residents live below this density.  But then I started doing the math for Chicago, where a block typically has 15 or so lots on each side of the street.  There are 8 Chicago blocks in a mile, so that makes 120 lots in that mile.  So how many lots are in a square mile?  Not 120 x 120, because lots are a lot longer than they are wide.  So a typical Chicago layout will have a block with 15 lots, but the perendicular block consists in the sequence from street to alley to street to alley to street, ie each "block" is really just half a block long, so each "real" block of 1/8 of a mile is four lots long.  That means that a typical square mile in Chicago has about 120 x 32 lots, so 3840 lots.  A square mile has 640 acres, so this amounts to only 6 lots per acre.  Anyway, many (most?) neighborhoods in Chicago aren't just single-family homes, they're two or three flats.  So we're talking maybe 12 households per acre.  But it's still a lot less than I'd initially though.  Consider that many areas of Chicago have industrial or commercial space without residents, and that even more areas are bombed-out blocks with only 3 or 4 intact houses per block, and Chicago's density goes down further.  In fact, if you take Chicago's 2010 population density of about 12000/square mile, and divide it by 640 acres, you get about 18 people per square mile, so only 9 households or so.

Anyway, the author says that, even if we simply attained this modest density of an inner-ring suburb, where many houses would still have yards to play in, we could substantially reduce the footprint of our cities, as well as all those lost costs that he describes.  The article includes a really cool chart showing population densities of major cities across the world.  Expectedly, the US is the least efficient user of space in its cities, followed by Africa and South America, Europe, then Asia, where they really know how to pack people in.  By my own rough calculation, Bogota clocks in around 65,000 people per square mile if you divide the actual urban area by the population (leaving out rural areas and uninhabited forests that are included in the official capital district), giving you about 100 people per acre, or 50 households an acre.  That's similar to Manhattan, and much denser than New York City as a whole.  Bogota certainly feels dense and bustling, but not suffocatingly so, at least not for me.  The small city where our house is in Colombia has about 36,000 people per square mile, so about 56 people or 28 households per acre.

I was curious about how my family's living situation compares to different population densities in world cities.  Our house in Colombia is big and sprawling compared to others, but even it gives 18 households an acre, and in our four-person household's case 75 people an acre.  If we divide this in half to account for streets and parks and such, we're talking about 40 people an acre, so similar to Mexico City or Rio de Janeiro.  Of course right now it's unoccupied, so it's just a big empty space driving down the density of living, breathing people in the town.

In this case of population density, our lifestyle in Washington is greener than in Colombia.  Our apartment in Arlington, Virginia holds five of us right now in 1100 ft2, or about 105 m2.  We're more crowded than we'd prefer to be, but by no means uncomfortable, and I think that between families and college students, most of the apartments in our building have a similar occupancy.  That would amount to about 216 people per acre, before even multiplying by the ten floors in our building.  So we're talking a density of about 2,160 people per acre of ground.  Even if you subtract out the parking lots, streets, parks and nonresidential buildings in our area, we'd still be talking a pretty high population density, like in the leagues of Mumbai on that article's chart, if the whole area was like our building.  I feel good about that--I like when people use space efficiently.  That said, much of the rest of our neighborhood is big single-family houses with driveways separating them, so you've got this weird juxtaposition of ultra-dense housing and then a very inefficient use of space.  I guess that's why the houses there cost twice what they'd be worth in Chicago--they're sitting on land that's begging to have like ten times the density!