Why self-driving cars will cause sprawl (according to an Italian Physicist)

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At 99mph, we think about the second-order effects of self-driving cars (aka autonomous vehicles or AVs). Last time we wrote about how AVs will bring about a $1 trillion shift in real estate across 13 major US metros — a phenomenon we call “The Great Flattening.”

In this post, we want to delve into the core claim— that AVs will result in massive sprawl — a bit deeper

To do so, let’s get historical. AVs aren’t the first new transit tech to come onto the scene. How have previous changes in mobility impacted the size of urban footprints?

Various urban footprints today. Source: https://geographyeducation.org/articles/comparing-urban-footprints/

You can’t have a conversation on this topic without giving a nod to the physicist Cesare Marchetti. On the side of his nuclear physics day job, Marchetti explored exactly this question.

In a 1994 paper called “Anthropological Invariants in Travel Behavior,” he looked at empirical historical data to establish a relationship between the adoption of new transit technology and how much the footprints of cities sprawl.

We think Marchetti’s concept is so important for thinking about AVs, that we made an explainer video on his concept of a Marchetti Wall. The remaining post gets a bit wonkier.

Thanks to the talented Arnie Deltoff for creating the video. animationdoc.com

tl;dr — Marchetti makes two core claims:

  1. Across cultures, time, and transit modality, people spend on average 1 hour traveling per day
  2. The footprint of a city is determined by how far an hour can get you in the dominant mode of transit

Introducing a unit of measure: The Marchetti

I’d like to do the old man an honor and name a unit of measurement after him: The Marchetti.

Let’s define our oldest mobility technology — walking — to be a 1 Marchetti technology. Marchetti observed that most ancient walking cities, like Ancient Rome or Venice, topped out at around 5km diameter (3.1 miles). We can say a 1 Marchetti technology allows cities to grow to be 3.1 miles wide.

We can then define, proportionally, how many Marchettis others forms of transit are by how far they allow a city to expand.

Illustration from Marchetti’s original paper

Here’s roughly where Marchetti placed a handful of other technologies based on empirical data of historical city size.

So, we have a simple formula: The predicted diameter of a city is 3.1 miles multiplied by the # of Marchettis.

Marchetti put the car at an 8 Marchetti technology that would create 25 mile diameter cities, assuming 25mph driving speed.

Is Marchetti’s actually right?

Let’s check to see if Marchetti’s law holds for car-centric US cities. We would look at two things:

1. Do people in car-dominant cities still travel ~1 hour per day?

If we equate transit time to commute, Marchetti nails it with his “one hour” rule.

Here are mean roundtrip commutes across US Cities from the Census’ American Community Survey.

Source: 2015 ACS 5-year survey for workers 16 years and over who did not work at home

The average person still spends one hour commuting in a car in major cities. Good on you, Prof. Marchetti.

2. Are cities ~25 miles in diameter (8 times larger than Old Venice)?

Here’s where Marchetti needs some updating.

US cities seem to be significantly larger than Marchetti’s Wall would imply.

Why is this? There are two flaws in Marchetti’s formulation, from what I can see:

  1. He considers the mean commute to define the size of a city rather the longest commute that a typical person might do.
  2. He assumes 40km/hr (25mph) as the speed of a car. In reality, road speed varies dramatically based on the city and direction of travel.

Let’s try to improve on Marchetti

The goal here is to figure out a way to predict the size of cities in response to a shift in mobility technology — in our case AVs.

Here is how we plan to update Marchetti’s core insight to build a better model.

  1. We will look at the longest typical commute rather than the mean. We will use the 90th percentile commute. It doesn’t actually make sense to look at mean commute to see how far a city extends because roughly half of people will go further than the mean.
  2. We will take into account actual car driving speeds in traffic. Heading West from midtown Manhattan (across the Lincoln Tunnel chokepoint) takes longer than heading North on solid land. Marchetti would not have had access to this data in pre-GPS days, but we do.

Example: How many Marchettis is car travel in San Francisco

Shamelessly leaning into my geographical bias, let’s try this for San Francisco.

Marchetti would have put San Francisco’s boundary here — a 25 mile diameter circle.

Marchetti’s predicted 25 mile diameter car-centric city … not what we need for San Francisco

Marchetti clearly knew nothing of rush hour traffic over the Bay Bridge.

Let’s start with the adjustment for commute tail rather than commute mean. We use 2015 American Community Survey data to extrapolate how long the 90th percentile commuter in San Fran travels.

So instead of looking for a 30-minute drive boundary, we are instead going to look for a 63-minute drive boundary to account for the least fortunate commuters amongst us.

The below map (green) is how far 63 minutes can get you in traffic in San Francisco. We use 5:30pm Wednesday traffic from City Hall as our origin. We’ve added a 30 minute commuting radius (blue) to show how far the average commuter travels.

For our purposes, let’s call this the current size of San Francisco. 63 minutes will get you a measly 16 miles going East over the Bay Bridge to Berkeley, while it will get you a respectable 45 miles going South toward Cupertino. The average distance that 63 minutes gets you is 29 miles at an average driving speed of 28mph.

Using our Marchetti formula, we can say that driving in San Francisco is a 19 Marchetti mode of transit, i.e. San Francisco has grown 19 times larger than ancient walking cities of yore due to the car.

How many Marchettis will AVs be?

Now let’s use our imaginations.

How many Marchettis would we expect AV travel in San Francisco to be?

We may come back to this in more detail in a future post. Suffice to say, AVs should be a superior mode of transit to human-driven cars and therefore have more Marchettis. We tend not to adopt inferior modes of transit.

Here’s the big leap: Marchetti focused solely on speed of transit. But might Marchetti’s law apply to other aspects of transit quality? I would offer that we should think more holistically about the overall quality of transit and not just the speed — comfort, convenience, reliability, and ability to multitask all matter. These non-speed dimensions are the ones where AVs hold the clearest promise.

Here’s one indication that comfort and productivity matter for travel tolerance: The behavior of tech workers living in San Francisco and commuting to Silicon Valley in their Wifi-enabled shuttles (~2.5 hours roundtrip). There are no shortage of good jobs in San Francisco proper yet ~10k voluntarily people make this reverse commute every day. I suspect very few would if they had to drive themselves.

Who are these millennials gathered on the street corner, face glued in phone? They are tech employees about to embark on their 2.5 hour roundtrip daily commute from San Francisco to the gilded office parks in Silicon Valley. But they won’t drive themselves. The Wifi-enabled tech shuttles have made possible a new behavior: A job in boring suburbs doesn’t mean you can’t live in cool city.

Scenario 1 (19 25 Marchettis):

Let’s suppose traffic stays constant and people are willing to travel 30% longer because they can now be productive (or relaxed and unproductive if they choose…) while in transit.

The 30% additional willingness to travel means AVs become a 25 Marchetti mode of transit. How far will San Francisco sprawl in a 25 Marchetti world?

Green = 19 Marchettis. Light red = 25 Marchettis.

Suddenly the beaches of Half Moon Bay or the slopes of Mt Diablo are now in play. So is cheaper real estate in San Pablo and Pinole. Maybe these options start to draw at people still paying pretty high rent to live 45 minutes away from SF in an unremarkable suburb?

Scenario 2 (19 35 Marchettis):

Taking a more aggressive scenario, let’s suppose AVs become a 35 Marchetti mode of transit. In this scenario perhaps driving speed improves by 40% (going on average 39mph) along with the 30% increased appetite to travel.

Green = 19 Marchettis. Light red = 25 Marchettis. Dark red = 35 Marchettis.

People familiar with the region will notice that some notable areas are now ensnared by the sprawl. Napa, Sonoma and nearly Santa Cruz. These are internationally-famous destinations and lovely places to live. If commuting routinely to San Francisco feels doable, you better believe people are going to take that opportunity.

And … for the ski bums and real AV enthusiasts amongst you, 63 Marchettis will get you to Tahoe.

Wrap-up

Okay, we’ve given ourselves a starting point for thinking about how AVs might cause our cities to sprawl. But a lot of this depends on what AVs will do to traffic. If AVs double the time it takes to move around, because the roads are clogged with people using their AVs as hotels, it may not end up being as many Marchettis.

But we would argue this likely won’t happen for a couple reasons.

  1. There’s a self-regulating feedback mechanism here. If traffic gets too bad, people will change their behavior. The number of Marchettis will decrease and people will move in closer. People moving closer in will reduce traffic. Likewise, if traffic improves, people will move outward making traffic worse. Because of this feedback mechanism, we should expect an equilibrium to be reached rather than out-of-control traffic growth.

2. Policy response: AVs provide a lever for policy makers to dial up and down traffic in the same way the Fed dials up and down the interest rate. They can charge a per mile usage fee to price contributions to congestion. Econ 101 says that pricing usage will decrease usage. I attended the excellent UrbanismNext conference in Portland this week along with dozens of policy-makers. There was almost universal acceptance that a usage fee of some kind is coming. Robin Chase’s “Shared Mobility Principles for Liveable Cities” lists fair usage fees as one of its core 10 principles. A number of government agencies and companies like Uber and Lyft have already signed onto this.

Nonetheless, what Marchetti tells us is clear. Land use and mobility are inexorably interlinked. And as mobility improves, we should expect sprawl.


Some shortcomings of the above analysis:

  • This analysis assumes monocentricity, a single city center. Cities are mostly not monocentric. A polycentric city will sprawl wider than a monocentric city because polycentric cities will produce additional loci of employment and entertainment.
  • 5:30pm departure time is arbitrary. A more detailed analysis might account for the distribution of departure times and the travel times for that distribution.
  • Public transit is not accounted for. Census estimates that 17% of workers commute by transit, in the San Francisco metro area. Rail is a subset of this.