As the student flies?


by Dr. Matthew Crespi

Welcome back to Transit Tuesday! Today we’re going to be taking a deeper dive at a common question that usually gets a short answer: Why do we use straight-line distances between transit stops and schools? (This is how we calculated distances on the SHSF Transit Map, and we plan to do so again on v2, the data cleaning for which is still underway.)

The short version is that “walking directions aren’t as reliable as people think they are, and with straight-line distances there’s a consistent downward bias that’s easy to think about as opposed to a noisy metric where people aren’t as familiar with the sources of variation.” That’s a true answer, and if it’s enough for you, feel free to stop reading. But if you want the full story, keep reading and we’ll break down our reasons.

First, walking directions can be awesome where pedestrian infrastructure is well mapped, and in dense cities and popular destinations, the infrastructure can be VERY well mapped, to the point where tiny walkways and even building interiors are available on services like Google Maps. But in most of the country, wayfinding services will default to the road network. This can create big errors in both directions: some roads are very dangerous to walk along, and assuming a pedestrian could safely navigate the side of a highway may result in substantial underestimates of the walking time, whereas assuming pedestrians can ONLY walk along roads may result in nonsensically long walks, such as this example of Google suggesting a 7.1 mile walk to get between two houses with less than a single lot’s width between them (found on reddit, first posted by a now-deactivated account).

Even when formal pedestrian infrastructure is well mapped, the dominant mode of travel may still be informal pedestrian infrastructure. A “desire path” is a path created by demand, often worn away by foot traffic going where pedestrians want the path to be rather than where it is. This photograph by Duncan Rawlinson (borrowed from the 99% Invisible page on desire paths) shows two converging desire paths mapping frequently taken shortcuts between where people frequently are and where they want to go.

An aside to a post that’s already an aside: planners — including schools! — can successfully use desire paths to create better pedestrian infrastructure. Grassy quadrangles and open common areas are common in campus designs at almost every level. Students walk across the open spaces to get to buildings, and paving those paths will make them accessible to students with walkers and wheelchairs as well (plus your buildings get less muddy when it’s wet outside). Ohio State University took this approach, paving the students’ desire paths:


Students can’t always use straight lines, though, so why do we? Straight line distances provide a lower bound. The walk between two points on a flat surface will never be shorter than the straight line that connects them (and yes, the Earth isn’t exactly a flat surface, and believe it or not, yes, we do take into account the curvature of the planet when calculating the surface distance between GPS coordinates, but at the scale of less than 5 miles it doesn’t really make a difference). It’s easy to think about the distances being “at LEAST” X miles instead of having to learn about where pedestrian infrastructure isn’t well mapped and thinking through which type of error might be more likely.

There’s another reason we use straight lines instead of walking directions: replicability. When we have GPS coordinates for a transit stop and a school, those coordinates aren’t always exactly on the network of roads and/or walkways. Using a service to calculate walking directions between them gets a little tricky, as it won’t always give a clean and entirely sensible answer when you’re not starting on the network. Consistently handling the questions of “where on the network do you appear and how do you get there?” isn’t trivial to implement. You might think “just use the closest point,” but sometimes that massively increases your walk compared to going out the more optimal door of the building, which introduces another source of noise, and it’s not clear that we’d get any real value from increasing the complexity and making our methods harder to implement, replicate, or adapt.

Take this example from a well-mapped dense American city with a solid community college system: Baltimore. Trying to get from the south side of this building (2901 Liberty Heights Ave) to the nearest bus stop results in an almost half mile walk (past, coincidentally and problematically, another bus stop):

But move the starting coordinates to the north side of the building, and Google suddenly has the student popping onto the main road, despite the previous directions deciding that was impassable:

The student in the second map gets to teleport across what Google was previously treating as impassable. In both cases, the student started in the same building and had access to the same exit doors and walkways.

Incidentally, in this case it turns out the shortcut IS feasible (at least for most pedestrians), due to a staircase that hasn’t been mapped into Google’s wayfinding database.

From Street View:

Starting on the different sides of a not-huge building shouldn’t be able to quadruple the length of a calculation. The issue is with how coordinates not on walkable paths get translated to the walkable paths. Collapsing an entire campus down to a single GPS point presents enough issues without worrying that the difference of a few feet inside a building could change the walking distance by a third of a mile or more.

All of this is why we use straight line distances (“as the student flies”). It’s “wrong,” but it’s wrong in an easy to think about way, as opposed to wrong in poorly understood and idiosyncratic ways. It’s a lower bound on the true distance, and it’s less susceptible to noise. The decision also makes it more reasonable to compare or compile across geographic areas with differences in mapping quality, which was really our initial goal when we started this project over a year ago: creating the first nationwide picture of the transit accessibility of America’s community and technical colleges.



Seldin/Haring-Smith Foundation (SHSF)

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