Wednesday, May 14, 2014

Of the importance of density: empirical proof

One of the main aims of proponents of a better urbanism is increasing density. Unfortunately, it's also one of the things that scare people used to low-density developments and who associate density with cities: congestion, crime, etc... This perception is pretty ridiculous for people who live in most cities, but it's still there. Some people ask: "Why are you so obsessed with density?", others are less polite and say "Why do you want to force people to live cooped up like chicken in cages?".

The reality is that what people like me want to do is not increase density for density's sake, the main goals are about:
  • Creating more sustainable cities where there are economical and environmentally friendly ways to get around instead of just relying on private motorized vehicles
  • Create systems with richer public realms so as to favor the creation of communities through regular social interactions
  • Make cities where it's just plain better to live because of a vibrant culture and a lot of activities, economical and cultural
It just so happens that some density is required for this. Alternatives to cars largely don't go as fast as cars, rapid transit can beat them, but only with stops being widely spaced, so you need density around them. So for these alternatives to be viable, destinations need to be closer to residential areas. However, you can't build a supermarket every 1 kilometer, each supermarket, like any store, requires a certain pool of customers to be financially viable. For instance, if supermarkets require about 7 000 people to stay afloat and you have a city of 20 000 people, you can sustain only 3 supermarkets at once.

So you can approximate how many stores you can have in an area by looking at the population. Some proximity stores like corner stores need few people to sustain themselves, specialized stores need a very large pool of customers, so they will need to be concentrated at nodes of regional transport system, whether boulevards, highway interchanges or rapid transit stations, depending on what people use to get around.

Let's take this example of a suburb with a population of 20 000 people in a perfect circle. The density of residential areas is 3 000 people per square kilometer (7 500 per square mile), typical of Québec suburbs, with only 80% of the city area being residential areas, the rest being parks, commercial, industrial, etc... We'll suppose that density is spread equally around. This city can sustain 3 supermarkets. Even if all three were placed to maximize proximity, only 10% of the population would be within a 5-minute walking distance from one, and 40% within 10 minutes.
A 20 000-people suburb with three supermarkets, 5-minute walksheds drawn around each one

Increase density to a respectable but still middling 8 000 people per square kilometer (20 000 per square mile), and it already looks much better. As the population is the same, the number of supermarkets they can support is the same, 3, and 30% of people are within a 5-minute walk from the closest supermarket, and everyone would be within 10 minutes of walking from at least one:
A 20 000-people small city with 3 supermarkets
Now build a dense urban neighborhood of 15 000 people per square kilometer (38 000 per square mile) and nearly 60% of people are within the 5-minute walksheds of the nearest supermarket, and a lot of people are within 10-minute walking distance from the 3 supermarkets.
A dense urban neighborhood of 20 000 people with 3 supermarkets
Now, this is a simplification, in reality you can have greater densities around commercial areas and the walksheds may be smaller because of less walking-friendly street grids, but it illustrates the principle. As you build denser, more things can be within walking distance which helps walking, of course, but also transit as the greater density means increased ridership and thus higher frequency.

An example of how density increases active transport modes and transit, and reduces dependency on the car

OK, right now, it's a pretty basic article about a basic principle. A bit of a bore I wager. However, I have more to offer.

In Québec, we have so-called "origin-destination" studies which question thousands of people in major agglomeration about their trips, whether to work, to school, for leisure or else. These studies include where people start their trips (origins), where they end them (destinations), but also their motives and their mean of transport (mode).

The studies split up the metropolitan areas in a variety of small sectors, each one getting a page looking like this:
Example of an O-D sector and its info
This page offers all the info to establish the density of the area as they not only offer the population and the area, but they also show the street grid, which helped me approximate exactly how much of each area is inhabited and how much is not inhabited (absence of streets or very rare ones). Like in this example, around 50 or 60% of the area would be inhabited, the rest is a park.

By inputing this data in an Excel worksheet, I've been able to create graphs showing how mode share changes depending on population density of inhabited area in each sector. And the results are telling. But first, for people who may not know, some hints:

  • Québec's metropolis, 1,6 million people in the city itself, around twice that including suburbs
  • Has 4 subway lines that are very used and very frequent, and a complete bus system with many frequent lines in the city itself, which they call the "10 minutes max" lines.
  • Commuter rail lines in the suburbs, but that only operate in the peak periods for the most part, and with pretty low frequencies
  • Québec's national capital, around 500 000 people in the city, which has swallowed many suburbs over the years, 700 000 people including the suburbs that have not been merged.
  • No subway, no tramway, no rapid transit. Just a few lines of "metrobus" which are essentially frequent bus lines with stops spread a bit further apart.
  • A LOT of highways, very car-dependent suburbs, but a well-preserved dense inner city with European-inspired areas
Final note, "mode share" for those who don't know means what share of all trips are made in a specific mode. So a 10% transit mode share means that 10% of all trips are made in transit.

OK, so in the following graphs, the sectors from Montréal are in red, those from Québec are in blue. I looked at the trips of residents, meaning trips (excluding returns) that originate from the sectors, and not those that ended in them.

First, how does transit use change with residential density?
Transit mode share (y-axis) vs residential density (x-axis, people per square kilometer)
The relation is very clear here, transit mode share seems directly proportional to density in Montréal. The odd point that is way over the trend at around 5 000 people per square kilometer is actually the downtown sector, in which few people actually live because most of the space is commercial and offices. In Québec City, there is also a positive trend, but it seems to max out at about 12 to 15%. There are two factors that may influence this:
  1. The absence of subway or other rapid transit line with high frequencies, which makes transit slow and much less useful. The subway seems to help the transit share even in relatively low densities, as sectors in Montréal with around 6 000 people per square kilometer (15 000 per square mile) have transit use about 50% higher than similarly dense areas in Québec City. Which shows the limited use of buses in mixed traffic to drive up transit use.
  2. Montréal is a bigger city, so even in the dense core there may be times where people need to take transit to go a bit further, whereas all the attractions in the urban core of Québec City may be closer together and thus be closer to dense areas, not needing transit to get there.
 Now let's look at active transport, walking and biking:
Active transport mode share (y-axis) vs residential density (x-axis, people per square kilometer)
Interesting here how Québec City's trend is actually over Montréal's. Maybe due to the lack of good transit option, people in dense areas may walk more and take transit less than in Montréal. Alternatively, the poor performance of Montréal may be mainly about denser suburbs between 7 000 to 10 000 people per square kilometer which are not that walking friendly (I live in one, Lasalle, walking to stores isn't impossible but not really pleasant). Note that some high-density sectors in Montréal do match similarly dense sectors in Québec City for active transport mode share.

Anyways, let's look at the car mode share to finish:
Auto mode share (y-axis) vs residential density (x-axis, people per square kilometer)
In both areas, the trend line is clearly linear, which actually surprised me to see such a strong linear relationship between density and car mode share. I expected it to decline as density rose, yes, but to see such a strong effect was even a bit strange, it seems too perfect. Yet, that is the real result.

Anyway, Montréal is the winner here, in high-density sectors, its car mode share is up to 10 points less than in Québec City's high-density sectors. However, the car mode shares in the suburbs are very similar. Despite Québec City's sectors having higher active transport mode shares, the much higher transit use, largely due I think to the rapid transit lines in Montréal, means that Montréalers in dense areas use cars to get around even less than the people in Québec City's dense areas. But they are more alike than they are different.

And again, that red dot in its lonesome far below the trend is Montréal's downtown area, which has little population but sky-high density in everything else (jobs, stores, etc...).

Despite the trend being clear, sectors with identical densities can vary in car mode share by up to 15%, so density isn't everything, even if it's a very strong factor. I guess the other factors that may lead to differences include:
  • If sectors have a lot of mixed use rather than use separation which increases distances
  • If the area has highways cutting it in half and allowing fast car movements
  • If sectors have good or bad transit service (in the case of Montréal, do they have access to the subway or not)
  • If they have street grids that favor walking or street grids which makes walking more difficult
  • If the population in the area is richer or poorer
I may do something like that later on, but for now, I think I'm quite satisfied with the results, which clearly show how density is a very strong factor reducing car use and increasing the rate of walking, biking and transit use.


  1. I think another factor might be the scale at which density is measured. People are generally willing to spend about 5-15 minutes travelling to shopping for instance (depending on what they're buying), which roughly corresponds to the size of these sectors. However, for commuting, most people are willing to travel 30 minutes, which can get you further. So Quebec's core and its outer suburbs are within reasonable commuting distance of each other, even when you take into account congestion. It might make sense to look at larger areas, maybe around 200 km2, and their density. Doing this with Quebec causes the core's density to be significantly diluted by the suburbs. In Montreal, fairly high densities are maintained across an area of about this size, so the densities of the core don't get diluted as much.

    If you have high densities at a smaller local scale, but low densities across a large scale, people might still find themselves communiting to/from places that are sprawled and autocentric to/from dense areas, and therefore travel by car. Once you own a car, you're more likely to use it. And once you're in your car, you're more likely to pick up your kids from school, or pick up groceries too (ie by car also) even if it might have been possible to do these other trips by foot or transit. And now that you're driving everywhere, it will influence the design of the communities, so that the built form and layout will still be auto-oriented, despite being dense.

    Also, I wouldn't look at the effect of density just in terms of incentivizing transit use and walking, but also as disentivizing driving. Dense areas with a same mode share as low density areas would have worse congestion, so driving mode share basically is forced to decrease until congestion become bearable. Dense areas also typically have less space for parking (especially if they're older). Even if you wanted to own a car in Saint-Jean-Baptiste, there seems to be no off street parking and on-street parking seems to be used to capacity.

    Anyways, maybe you could get a better correlation if you used trip generation density instead of population density. Trip generation density would take into account job density, and density of ammenities like retail, universities, hospitals, etc. That should move downtown Montreal closer the line of best of fit for instance.

  2. Another way to look at densities at a broader scale. Say you live in the Plateau. There's quite a bit within a 40 minute transit trip, basically the whole urban core. You can access double the land area accessible in 40 minutes by car, but if you look at the ring of land that using a car adds, it's mostly low density, and fairly residential (no destinations like shops or jobs), so the % increase in the amount stuff accessible to you is not much.

  3. Question: what do you think about a true "garden city" scenario, where exurban villages are surrounded by agricultural greenbelts protected from development by restrictive zoning? In such a scenario, the radius of the village could be limited by walking distance from a commuter rail station, and absent expressways drawing commercial development to the periphery (hello, Walmart!), people would be disinclined to drive to shops or work.

    Do you think such a situation is impossible to sustain because the economy of scale would not exist for local retail? Or is it too dependent on a "perfect storm" of planning regulations? Is it exclusionary because housing would become prohibitively expensive? I think Ebenezer Howard's Garden Cities of To-morrow could conceivably exist and sustain themselves if it weren't for all those damn cars! Automobile dependence is a self-fulfilling prophecy and a self-reinforcing problem.

  4. I don't know... A lack of expressways is not necessarily enough to discourage people from driving. If the next town over is 10 miles away and connected by a 2 or 4 lane road, I'd think plenty of people will use it to commute. You'd have to have either no town or suburb within 40+ miles, or really low quality dirt roads only. Plus, the variety of shops might be more limitted than some would like in a town that is small enough to be within walking distance of a train station.

    I guess if the town was fairly dense, you could have a decent amount of services, with rowhouses (with gardens), maybe up to 20,000 people within a 10 min walk. However, I'm not sure you could realistically support a town of 20,000 with only dirt roads, since you'd still have to get goods into town somehow. Most exurban areas are not that isolated, most will have towns within at least 10-20 miles. Maybe in the American (or Canadian) West, you could create a town that is this isolated. Still, if we're talking 40 miles to get from the town to the suburban fringe, and 20 miles from the suburban fringe to downtown, that might be something like an hour of commuting. Now in cities like Denver, Calgary and Phoenix, there are single families just miles from downtown. Plus, you'd have to built 40 miles of rail just to serve 20,000 people. So in summary:

    -You can live in a garden suburb where you only have access to the jobs that exist downtown or in your garden suburb... or you can live in the city or regular suburbs where you have access to jobs in the whole metro area. The number of jobs in downtown Phoenix is a pretty small fraction of the metro area total, although Calgary is better.

    -Same goes for shopping, but no-one's going to spend 60 minutes one way, 60 minutes back to go shopping, so shopping in the city would have to be combined with a work trip. But what if you want to shop with someone who doesn't work downtown (ex your kids, or if they're teenagers, maybe they'll want to go alone)? Or what if you want to do shopping on the weekend (since you don't have much time between 5pm and dinner time, especially if it's a 60 minute commute)? Then you're limitted to shops in the garden suburb. Or you could live in the city/suburbs and have access to all of the metro area's shopping.

    -You can live in a townhouse with a back yard in the garden suburb... but you could also live in a townhouse with a back yard, or even an SFH within a couple miles of downtown Calgary, downtown Denver, etc.

    Are people really going to pay enough to live in this garden suburb to justify building 40 miles of commuter rail?

    1. Admittedly, the assumptions about rail subsidies and total metropolitan populations used by Evenezer Howard are a bit… unrealistic. At the same time, much of Wisconsin, for example, has managed to remain clustered around small towns, rather than sprawling around cities, though with really poor public transit. (Thank you, Scott Walker…)

      Mainly I was noticing that exurbia like this, if centered around older towns, can retain a lot of the quality of life lost with contiguous sprawl. The situation in Wisconsin may be dependent on a relatively high rural population density to begin with, though, that you'd find more in the lower Midwestern United States (Wisconsin to Iowa to Ohio) than anywhere else. It wouldn't work so well in Nebraska or Utah, for example. But it probably works in Vermont.

      Not everybody likes big cities. (Though I certainly do.) Granted, although of these places are seeing slow but steady population loss as young people urbanize for better opportunities, this was the way the Midwest was "supposed to be" ever since Thomas Jefferson's Land Ordinance of 1785.