Hypothesis: Regular frequent transit service remains feasible even in single family homes in neighborhoods with a modicum of density.
The Land Use
Consider the 1 mile grid landscape that is common in the post-Revolutionary United States due to the Northwest Ordinance and the ease of development. The is roughly the streetcar era land use design.
While there are a variety of ways this grid can be carved up, one common way is to have
- 10 cross-streets per mile of grid long direction (520′ )
- 20 cross-streets per mile of grid in short direction (260′ )
This arrangement produces 200 blocks per square mile. The size of each block is:
- 520′ x 260′ block (center line – center line)
- 480′ x 240′ block (edge to edge), allowing space for roads.
If houses have a 40’ frontage with 110′ depth ( allowing 20′ for alley?) = 4,400 sq. ft. (~1/10 acre)
Note there are 640 acres per square mile and 43,560 square feet acre per acre.
This spacing gives 12 houses per block face long direction, or 24 houses per block. In this configuration, no houses face the short direction. Obviously this can be adjusted.
If there were only housing, this would give 4,800 houses per square mile
At 2 persons per household (which is definitely on the low side for single family homes, this gives us 9,600 PPSM in single family homes at typical built density. At 5 persons per household, this leads to 24,000 PPSM.
At 5 persons per household, we could increase lot size to 1/4 acre (neglecting roads) and still can get 2,560 houses per square mile or 12,800 PPSM.
While some space is devoted to schools, parks, retail, commercial, and industrial activity, among other uses, I hope this is persuasive that 10,000 PPSM is feasible over large areas without being Manhattan-like high density. The City of Minneapolis for instance according to the 2010 Census has a density of 7,417 PPSM. At its peak population, it had over 10,000 PPSM.
The target density for successful transit is often given as 10,000 persons per square mile (PPSM), as per Zupan and Pushkarev (also discussed here).
If we assume that every person originates lots of short trips (which can be dealt with by walking or biking) and one long trip per day (say going to work), the 10,000 PPSM would generate 10,000 transit trips per square mile. So we have 10,000 Boardings. This is roughly streetcar era demand in cities.
If we space transit routes on the 1/2 mile routes (as was typical of streetcars) both east-west and north-south, with stops where transit routes crossed and half-way between (i.e. 1/4 mile spacing between stops), the area is served by 21 stops. The four stops at the outer corners are shared with 4 other areas, and the 8 non-corner stops at the perimeter are shared with 2 other areas, while 5 stops are internal to the 1 mile square, gives us 12 equivalent dedicated stops for the area.
With 10,000 PPSM and 12 stops, each stop serves 833 people per day. If transit vehicles carry 50 people each, that is 17 full transit vehicles per day. Of course transit vehicles do not generally fill up at one transit stop, and over a 17 hour day, this would be 1 transit vehicle every hour. If instead we wanted service at 10 minute headways, but full vehicles, we would expect each vehicle to fill up 1/6 of its load at each stop (or about 8 passengers per stop). That would be a much higher load factor than generally observed.
The maximum walking distance to a transit stop would be (by Pythagoras SQRT of 0.25^2 + 0.25^2 =) 0.35 miles.
So what guarantees people will make 1 transit trip per day? If there is no good alternative, this is an easy choice. Today, this depends. The argument for using transit is that in our idealized grid-like city with a grid-like transit system, the transit system is as direct as every other mode, so there is no lost distance due to circuity. The only lost time is the schedule delay (which is a maximum on average of 5 minutes, less if people can time their wait to match the transit vehicle), and the time when the vehicle is stopped (and accelerating and decelerating) boarding and alighting passengers, which we know can be faster if people pre-pay, and the transfer time between vehicles (with a maximum of one transfer in the idealized grid, again with a maximum on average of 5 minutes, less if the routes are timed well). Finally with any transit advantages (e.g. signal timing priority, exclusive lane or stopping in lane, as opposed to weaving into stops) transit can recover some of the time lost vis-a-vis the automobile.
Where transit is better (faster, cheaper) than alternatives, and frequent enough, people will use it in large numbers. This is observed daily in large cities. Thus it must be feasible to obtain such faster, cheaper, frequent enough service levels. In most places in the US, the transit service and ridership is not there. Let’s work through an example.
For a five mile trip, there will be about 20 stops at 1/4 mile stop spacing. If each stop results in 30 seconds lost time (2-3 seconds per boarding plus acceleration/deceleration), that is 10 minutes of time lost there. This will generally be slower than an automobile, even with stop signs or red lights every 1/4 mile, as the time spent stop at the stop will be less than for transit, even with pre-payment. (Unless the auto is stuck behind a transit vehicle and cannot pass).
Initial schedule delay is 5 minutes assuming random arrivals.
Walk access time of (let’s say 1/2 of 0.35 miles or 0.18 miles at 3 miles per hour) is about 4 minutes. This is obviously farther than from the front door to a parked car at the home end. Destination walk egress time is probably similar for most people. For transit to downtown, lower for transit (and higher for the parked car).
Transfer time is also non-trivial, and can be as high as another 5 minutes if it is effectively uncoordinated.
So now even with our idealized transit system we have lost something like 10+5+4+5+4 minutes or 28 minutes compared with the car for a 5 mile trip. At a value of time of $15/hour ($0.25/minute) this is the equivalent of $7. If the transit fare is $2, and the cost of gas (at $5/gallon and 25 miles per gallon) is $1 (not even considering carpooling), net additional out-of-pocket cost for transit is now the equivalent of $8. Of course, vehicle ownership ($10-$20/day) can be avoided, as can parking charges. We are not considering externalities, and other costs of vehicles that are not internalized.
We can make transit faster with express routes on limited access rights-of-way. If demand is high enough, we can make transit go faster, or have an even higher frequency, and stop less often. One disadvantage of express routes is a longer access/egress time (they can’t be spaced as close together if they are to achieve economies of scale, so they are on the mile instead of 1/2 mile spacing at best (as per London)). If that access and/or egress is by transit itself, that imposes additional scheduling time penalties. We can compensate because now our land use changes to take advantage of the express services. At express stations, densities rise. Apartments replace single-family homes. We can also give transit a higher frequency. Express buses and commuter trains often have low frequencies, while modern or modernized subways may have one train every 2 minutes or better. So if we increase the highest distance to a station for 1 mile spacing between stations and 1 mile between routes (so every station is a transfer), the walk access time is 1/2 of the maximum time of SQRT (0.5^2+0.5^2) = 0.71 or 0.35 miles. At 3 mph this is a walk time of 7.1 minutes on each end.
For a 5 mile trip with transfer Our lost time is 2.5 (30 seconds [per stop * 5 stops]) + 1 (schedule delay) + 7 (access) + 1 (transfer delay) + 7 (egress time) = 18.5 minutes. This is less than the local transit service above, and can be reduced for people who live closer to the station rather than spread out uniformly across the landscape. If we have higher travel speeds than auto (let’s say averaging 45 mph while in motion on exclusive right-of-way instead of 30 on surface streets), for a 5 mile trip the express transit time is 6.67 minutes instead of 10 minutes. But this 3.33 minute savings does not outweigh the lost delays due to access and waiting costs. This does not even begin to consider the additional costs of operating express vs. local services, or revenues from the service.
To reduce transportation costs with transit-like services, we can arrange cities linearly, thereby eliminating transfers and reducing access costs. This wastes accessibility for non-transit modes. So optimal urban form depends on the technology you are optimizing for. In a city where driving is perceived to cost $1/trip, and it saves between 18 and 28 minutes per trip, it is no wonder the automobile is the dominant mode for long distance trips even in historically transit advantageous places. Changing that requires changing the perceived (and real) cost of driving for drivers, as there is little that can be done on the transit supply side which will make a significant difference in the absence of that for most markets.
In dense areas, the market takes care of that, with expensive parking. In low density areas, there is enough room for everyone’s car without charging.
I believe systematically re-arranging existing cities for transit (or any mode) is putting the cart before the horse. Transportation should serve activities, and while transportation and land use co-evolve, that co-evolution is slow (over decades) and should be adaptable to alternatives.