It is likely that there is, but this seems not to be the case in other, more densely populated localities.

People walking around at Westfield WTC, New York. Photo by Kai Pilger; public domain.

As the second wave of the coronavirus arrives, I was part of a discussion where keeping a healthy distance from others came up as a topic. Someone said:

I am really glad not to live in Manhattan — it’s so densely populated that if everyone went outside they could not even stay six feet apart!

While this statement was obviously just a figure of speech, it really piqued my curiosity: Manhattan is really densely populated — what if people really don’t fit on the streets if they want to keep a decent distance? I decided to investigate this question using publicly available geo data.

Data for the analysis

If we want to answer our research question, we need three pieces of information:

  • Boundaries of preferably small spatial units (e.g. neighborhoods) to be able to show variance across the city;
  • Population information about these spatial units;
  • Land cover data. “Outside” is only a subset of the city’s area — a large part is taken up by buildings, water, and other things.

Luckily, New York has an extensive repository of open data, and all of these are available: Neighborhood Tabulation Areas in a spatial data format; Population by NTAs in a spreadsheet; and Land cover data as a spatial raster dataset. I used a 3-feet resolution version of this data for my analysis as it is much smaller and faster to work with, but a newer and 36 times more detailed dataset (with more land cover types) is also available.

New York geo data: polygons of neighborhoods; land cover raster data; close-up of the land cover layer. Data from NYC OpenData, figures by the Author.

Tools

I am a big fan of reproducible research. Therefore, I wrote the analysis in an iPython notebook that you can find here. It has everything in it from downloading the data to calculating statistics and drawing maps. For those familiar with geographical analysis in Python, it won’t be surprising that my main tools were the GeoPandas and rasterstats packages.

Analysis & results

Areas and population

A crucial assumption for this analysis (and thought experiment) was that people need to stay in their neighborhood when they leave the house. If we let them go to (and fill up) parks, airports, docklands, cemeteries, etc, we might as well let them spill out of the city limits (as administrative boundaries are completely arbitrary¹). This, in turn, would ensure that there is enough space for everyone and it would be impossible to end up in a situation where there is not.

Therefore, I look at the data on a neighborhood level and ignore neighborhoods which have tiny populations compared to their size — ones like the examples I gave above. So, for example, Central Park is out.

Since the data I downloaded is nicely maintained, I can simply join the boundary geo data with the population data.

Usable outdoor space

The next step of the analysis is to identify the available outdoor space for each neighborhood. The land use layer has seven categories: 1: Tree canopy, 2: Grass/shrub, 3: Bare soil, 4: Water, 5: Building, 6: Road/railroad, 7: Other paved surfaces.

It is not immediately obvious which of these land covers can be used for our analysis. I decided that #1 and #2, while not entirely open spaces, qualify for this. Even if there are trees, we can scatter people among them in a way they can keep their distance. There is one caveat related to trees: their canopy could overlap shorter buildings, but this is probably a small problem that I assume away. #3 is obviously relevant, #4 and #5 are obviously not applicable. I categorize #7 as suitable as well — these are parking lots, courtyards, etc. The tricky category is number #6, “Road/railroad”.

On the one hand, this category is important, since roads are the immediate spaces people go to when they leave the house. However, not all road surfaces are usable — some are actually used by cars to move around.² And, as the name of the category says, some of these areas are used by railroads. As an expert estimate, I take 50% of the area of this category into account.³

Packing circles

“The most efficient way to pack different-sized circles together is not obvious.” — says the caption of the same image on the Wikipedia page for circle packing. Photo by Scott Bauer, public domain.

Since local recommendations related to distancing use imperial units (suggesting staying 6 feet apart), I used this distance in my analysis. Every person needs to have an empty circle around them that has a radius of 3 feet. However, since same-sized circles cannot be packed perfectly — there will always be some space between them — people will take up a bit more space if we want to ensure that nobody is closer than 6 ft to another person.

The area of a circle whose radius is 3 ft is r²π=28.27 ft²; according to Wikipedia, we have to divide this by 0.9069 to get the actual size of the occupied area when circles are packed — the result is then 31.18 ft².

Density in neighborhoods

The last step is to calculate for each neighborhood how much usable space a resident gets. If this space is less than 31.18 ft², people would not fit on the streets.

Unfortunately for our breakthrough results and fortunately for the residents of New York City, there are no neighborhoods where there is not enough space to keep enough distance.

Even the most dense neighborhood, Yorkville has almost three times as much space for people as the minimum required for keeping six feet distance.

Maximum distance

We can also look at our research question at another angle: what is the largest possible distance people can theoretically keep if they are all on the streets? This is very easy to calculate (see the notebook). For this metric, I return to the metric system (pun intended) and calculate this distance in meters.

Maximum distance (in meters) that people could keep if everyone went out to the street. Figure by the Author.

I show this value per neighborhood on the map for the neighborhoods of New York City (except for Staten Island, where population density is much lower than in the other four boroughs).

The value on this map is twice the radius of the “safety circle”: the actual distance between people. We can see that people in Manhattan have about 3.5–7 meters between them depending on the neighborhood. Measure out 3.5 meters in your home: it is really not that much! As we travel farther from the city center, population density decreases and consequently the maximum possible distance between people increases.

Closing remarks

While I did my due diligence when writing this analysis, it should not be taken entirely seriously — it is more of a fun personal project than actual research. Since there were many assumptions about the data, the results are not 100 percent certain.

For example, if we used a more detailed dataset — and preferably a vector-based one — for land cover, we could get the actual usable area and we could fit circles in a way that relax the assumption that the full “safety circle” has to be within the usable area. Such data were not available for New York City. However, there are places in the world, where it is, for example, the Basisregistratie Grootschalige Topografie dataset in the Netherlands would be suitable for this purpose

Ultra detailed land cover data from the Netherlands: the BGT dataset. This segment shows the “road parts” layer: paved areas, pedestrian and cyclist paths (greens, yellow-green); parking spots (purple); pavement (blue); public transport areas (sand); and areas occupied by railways (reddish); Figure by the Author — created using QGIS.

In any case, I feel that the research question is a valid one in the current global pandemic: there could easily be places on the globe where there is not enough space for people to go outside and keep their distance. After all, New York City is not even on the list of top 50 most densely populated cities. NYC’s densest borough, Manhattan has an overall population density of 26,821 people per square kilometers. Manila, the capital city of the Philippines (and the most densely populated city according to the table linked above) has an overall population density of 46,178 ppkm². It is very well possible that its densest parts do not have enough outdoor space.

Or, an even more extreme example is Dharavi, a locality in Mumbai, India, which has more than 1,000,000 people living on 2.165 km² — a population density ten times higher than Manila’s. Here, people could not keep sufficient distance outside even if the whole area was completely empty. There are good news though: against all odds, the leadership of Dharavi has been quite effective in combating COVID-19, according to a recent report by Bloomberg.

Notes

¹ Just look up the city limits of Paris or Las Vegas. These probably do not coincide with your mental map of these cities.
² Some might argue that the share of such areas is too high (i.e. the city could have fewer (or narrower) lanes. Discussing this statement is not part of this analysis
³ The above-mentioned 36-times more detailed dataset has railroads as a separate category, but it would require considerably more computing power. Additionally, using that dataset would not solve the problem of the separation of pavements, roads, parking spots, and other types of road elements, some of which can be used by pedestrians and some of which cannot.
Another reason for using imperial units here is the fact that the source data uses a projection based on it.
This setup also assumes that people cannot stand right next to the edge of the available space (e.g. next to a wall) but their whole six feet wide bubble is within this area.
We can simply add a buffer to the relevant areas and fill this buffered shape with circles with a 6 feet radius.


Is there enough space in Manhattan to stay six feet apart? | by András Hann was originally published in Towards Data Science on Medium, where people are continuing the conversation by highlighting and responding to this story.