The T’s 2024 marathon schedule

[updated with post-race experience in italics]

I’m not running the Boston Marathon this year. It’s not for lack of interest: I ran a 2:59:56 last year, my best finish in Boston (by time) and an improvement of 11 seconds over my previous best (and first) race in 2015. I thought it would be plenty fast to qualify, but the weather was good enough last year (fun fact: with more than 13,000 qualifiers more than 51% of finishers requalified. and it had the single highest number of Boston qualifiers of any race, ever), and new sponsor Bank of America stingy enough (apparently they took more sponsor bibs, so the number of qualifiers accepted was about 1000 fewer than previous years) that I missed out. By 24 seconds. Or, since I am in the final year of an age bracket, by 3 months and change. 

(As you can tell, I am not bitter about this at all. It would be exceedingly petty to hope for temperatures in the low 70s for the race, but it would also mean that the -7:20 qualifier I ran last fall would be almost a shoo-in if Boston had 4000 qualifiers instead of 14,000. I will make no further comment as I check a weather model. But who am I kidding, it will be 48˚, dry, cloudy with a 20 mph tailwind with my luck.) [it wasn’t, so I have a shot next year]

It does mean that I’ve had extra time to look at the T’s somewhat impressive marathon schedule. For the first time since 2019, the T has the resources to provide extra service, and this is on top of a schedule which already has more frequent midday service. With 64 total trains, it is likely the busiest day on the Worcester Line since the 1950s (at a time when they had four tracks to Framingham before the Turnpike cannibalized two). In addition, several trains have been extended to Southborough, making taking the train to the start a much more reasonable proposition. There are basically trains every 20 to 40 minutes in both directions, so spectating runners in three locations is somewhat reasonable. Plus, there’s a $10 all-weekend pass, so you can hop on and off basically for free. (They are undercharging for this; it should be a separate fare for Monday, but they probably don’t want to have to sell more tickets. It’s good for ridership, at least.)

So with no further ado, here is Ari’s Official Guide to the Railways on Marathon Monday. A couple of notes.

  • I use train numbers here preceded with a “P.” At least back in the day, trains on the Worcester Line were numbered with a “P” by CSX designating them as Passenger trains. This naming convention makes the text a bit more readable. Also Dave does this, so it is the right thing to do.
  • Three-digit train numbers (e.g. P518) are normally-scheduled trips. Four-digit numbers (e.g. P7564) are extras or have changed schedules.
  • This all assumes that everything runs on schedule. So, you know, take it with a small grain of salt. [especially after about 10:00, trains experience 15-25 minute delays between Framingham and Wellesley Hills because without level boarding, it takes a lot of time for people to get on and off]
  • In Wellesley, I sometimes refer to the stations as “Square,” “Hills” or “Farms” just so I don’t have to type “Wellesley” so much.

If you want to watch the lead men:

Arrive on any train in Framingham before 10:00. There are trains departing at 10:08 and 10:35. The 10:08 train (P7556) will depart almost exactly when the lead men’s pack arrives; you may be able to watch from the train as you roll out of town (the men may outpace the train for the first few hundred yards). The 10:35 (P7564) train will depart after the lead men (and women) are through and when the first Wave 1 runners begin to arrive.

If you take the 10:08 train, you can get off at Wellesley Square (10:23) or Wellesley Hills (10:26) to catch the lead men, who should arrive at Wellesley Square around 10:31 or 10:32 and Hills a few minutes after. P7564 departs Hills at 10:53 if you want to attempt to catch the runners again. The lead women will probably arrive a few minutes later; train P7514 (11:13) will allow you to comfortably watch the lead women run through. These trains will get you to Lansdowne by 11:17/11:37. The first would allow you to get to Lansdowne in time to see the lead men, the latter unlikely.

(Rosie Ruiz would be proud!)

Speaking of women, if you want to watch the lead women:

Arrive in Framingham by 10:15 (train 7653 arrives 10:14). Train P7564 will depart after the lead pack of women has gone through and get you to Wellesley Hills at 10:53, a couple of minutes before they arrive there. Train P7514 will leave Hills at 11:13, and get you to Lansdowne in time to see the lead women a third time quite easily.

If you want to watch a first-wave runner with a 3:00 or faster (given the depth of this year’s field, the entire first wave qualified under ~3:01).

You will still need to be on train P7563 and arrive in Framingham by 10:14, so you’ll get to see the lead women (get there earlier and you’ll see the lead men, too). Your runner should pass in time to take P7514 inbound at 10:55 and get you to Wellesley Square/Hills at 11:10/11:13. From there, P7516’s departure at 11:45/11:48 will give you plenty of time to get Downtown; even P7568 half an hour later would do the trick if your runner is running slower than a 2:50 or so.

If you want to watch a second-wave runner with a 3:15 finish time:

You’ll want to arrive in Framingham by 10:47 (although, of course, you can get there earlier to watch more) on P7513. Your runner should pass through well before 11:30, allowing you to take train P7516 and get to Wellesley Square with plenty of time to cheer. From there P7568 will get you downtown to see them finish.

The third wave is much more spread out with finish times spanning an hour between 3:25 and 4:25. Here are some scenarios:

3:25 runner: P7565 out arriving Framingham at 11:19 (or earlier, of course). P7568 inbound at 12:05, P518 inbound at 12:55 from the Wellesleys.

4:25 runner: You still probably want to arrive in Framingham by 11:19 as above. Depending on the time to cross the start line and your runner’s speed, they will clear Framingham around noon; if so, you can catch the 12:05. Otherwise the 12:40 train (P518) should get you to Wellesley in time to watch them there; you may want to ride it to Wellesley Farms and jog to the course to get ahead of them. From there, you may wish to walk to Riverside and take the Green Line downtown, although the Green Line is often quite slow on Marathon Monday.

For Wave 4 runners, the finish times are even more spread out. A Wave 4 runner may be a charity runner without a qualifying time and run faster, or an older runner with a slower qualifying time running a 4:50 race or slower. In these cases, consult the schedule.

Are you a runner who wants to skip the buses and take the train out?

I’ve never done this, but with the schedules this year it seems quite reasonable. There is a spectator shuttle from the state park near Southborough to Hopkinton and, apparently, to the Commuter Rail station as well. [There is definitely a shuttle from the Commuter Rail Station!] For spectators this might mean that you could watch the start, take a bus to the train station, and potentially see your runner a fourth time (although taking the bus to Southborough and then the train to Framingham in 40 minutes would be tricky; this might work better for later waves and then only if the timing is perfect, you could at least make it to, like, Natick).

But to get to the race, sure, why not? The “athlete village” at the high school is a glorified port-o-let line; and there are plenty more of these near the start line anyway behind the CVS. You could probably even have someone travel out with you to the start spectator area, take your gear, and see you off. (They could drive you there, too, but where’s the fun in that).

Trains P7507, P7561, P7509 and P511 arrive in Southborough at 8:11, 8:45, 9:12 and 9:53, about 50 minutes from Back Bay (and 40 from Boston Landing). Given the convoluted route the buses have to take to get to the high school, this may actually be faster than taking the bus, especially if getting Downtown would require some backtracking. And you’re not crammed into a bus designed for 6-year-olds worried that the driver is going to get on 495 north and wind up in New Hampshire. (Yes, this happened. In 2022 my bus driver—the bus itself was from Methuen so the driver was not familiar with the area—wound up on 495 north. No one batted an eye, because no one was from the area. I made my way to the front of the bus and guided the driver through the cloverleaf at Route 9 and back south to Hopkinton.)

So would I do it? I’m not entirely sure. [Most assuredly.] I trust the T well enough, but I guess the question would be getting from the T to Hopkinton. If all else fails, it’s a 2.5 mile warm-up run (albeit uphill). [I saw people doing this] I assume the buses would run as advertised and I would bet one could be flagged down on the road from the State Park (if they aren’t running to the train station). [Probably couldn’t flag one down, but definitely could take one from the train station.] It looks like you can get into the corrals from Cedar Street [Yes, you can walk right in, it’s kind of a VIP area with some charter buses parked nearby but they don’t seem to discriminate and/or probably assume you’re special, too.], otherwise from South Street would probably work. I’d leave at least an hour to get from the train to the start, but for a Wave 1 runner, leaving Boston Landing at 7:31 might be far preferable to being on a bus at the Common at 6:45. 

If I get in in 2025, and the T runs the same schedule, my plan is to take the 7:56 train from Boston Landing arriving at 8:45 at Southborough, and get on a bus there to the start. The next train (8:31-9:11) should work fine but having some buffer is nice. The earlier train would give enough time to walk back to the Athlete’s Village but there’s really no need to do that. If the weather is awful and I really don’t want to wait in the rain I might consider taking the bus, since there’s usually somewhere dry to wait at the start. Plenty of johns at the CVS.

Perhaps I’ll have to go out and do some reportage on the transit situation myself. Enjoy the race, and if you’re running, you’re welcome for the weather. [yeah, sorry, no one die at the finish line please]

A few notes:

  • Train numbering convention is that trains running to Worcester begin with 500 and theoretically range up to 549. 550 and up are Framingham turns. Even east, odd west.
  • There’s no express service in the morning. So there’s half the overall frequency of a normal weekday morning, although each station has about the same number of trains, the express trains run local. Service is then redistributed across the midday.
  • Previous marathon special service was basically to keep the normal weekday schedule and add a couple of trains in the middle of the morning. This increases service all day long, on the baseline of already increase service (2019 base schedules had four trains between 9 a.m. and 4 p.m., current schedules have hourly service, and the Marathon service this year has 14 trains in this timeframe, double the 2019 Marathon schedule and the normal 2024 schedule and more than triple 2019’s base schedule).
  • Service has also been extended out to Southborough much of the morning, and then as the race moves east, trains turn in Framingham. This really shows that some thought went into making the schedule.
  • With 63 trains calling at the Wellesleys and at Natick, this will likely be the most trains to stop in Wellesley in the 190 year history of the B&A. There were more trains in 1950, as far as I can tell, but many of them were express and intercity trains (plus, there were still four tracks east of Framingham back then).
  • The current schedule has 66 trains including the Lake Shore. 1952 had 64, 1950 had 68, 1947 had about 80, 1945 had 94, with nearly hourly service to Springfield (better, if you include local trains). Boston to Springfield in 2:10. Even the 1937 schedule, with about 120 trains daily, and the 1927 schedule, with 160 trains per day (!) has less service to Wellesley. (The 1927 schedule had 8 to 10 local trains between Boston and Riverside between 5 and 6 p.m., running subway-level service on that portion of the four-track railroad.)
At its peak, the B&A ran more service than the Marathon Schedule. Except to Wellesley and Natick, they’ll see the most stops ever on Marathon Monday. (This doesn’t even include intercity service. Also note the Saturday-only midday outbound service; this was back when a regular workweek was five weekdays and a half day on Saturday.)

The eclipse and transportation

Subway stations with long escalators usually have three. There are three escalators in Porter Square in Cambridge, and in all (or most) of the long-escalator Metro stations in DC (those don’t have stairs, even). This is mostly so that when one is shut for maintenance, there is redundancy for the others to run. But when all are operational, generally two run up and one runs down.

There’s a good reason for this: escalators are a natural bottleneck, and people arrive at a station pretty much randomly in a steady stream. But people depart stations in clumps: trains arrive and people get off all together. Even still, there can be queuing at bottlenecks where people have to slow down or navigate something which causes them to change their speed. Like getting on or off an escalator (or stairs).

So, there’s an eclipse on Monday. (I promise this is related!)

  • First thing first: the eclipse is totality or nothing. 99.3% = 0%. You have to go into totality, and preferably far enough in that you get more than two minutes of totality.
  • Second thing second: avoid clouds, and don’t plan ahead beyond “eclipse day.” In 2017, my father and I were in Louisville with family. The eclipse path there passed from Missouri to South Carolina, and we were prepared to drive any distance in any direction to see it. Turns out that we were able to go towards our intended destination (Chicago) and it was worth it.
  • Third: You do not need to go to where a bunch of other people go. Or somewhere specific. No matter where you go, if it’s clear, the sky is the sky. (Okay, climbing Mount Mansfield, which isn’t really allowed this time of year anyway because the trails are muddy, might let you watch the eclipse shadow approach over Lake Champlain at 1100 mph, but also is more likely to be in the fog.)
  • Expect spotty cell coverage at best. Rural areas may already be uncovered, but even the towers there might be completely overwhelmed. Pack a map, and snacks.

I’m very excited about seeing the eclipse. It’s a brilliant celestial event which occurs once every few years-if-not-decades with reasonable travel distance, it’s not commercialized, it’s a great communal event. And … I’m almost as excited about seeing what happens to traffic afterwards because this is a once-in-a-lifetime event and we really have no idea how it is going to play out.

Traffic happens because of the intersection of two elements: volume and bottlenecks (in another sense, demand and supply). A lane of traffic has a theoretical throughput of 2400 vehicles per hour, although this is rarely achieved. Once it becomes saturated with traffic, both speed and volume decreases; this process can take place solely based on volume around 1600 vehicles per hour (or a bit higher). Volume drops to 1000 or even less, with low speeds: this is called “Level of Service F.” (Far too often we plan roads around avoiding this by building oversupply rather than trying to manage demand.) Bottlenecks can cause additional queuing, and this isn’t solely lane drops: merges can be just as bad, as can what I call “sorting” where vehicles approaching an exit have to change lanes. Given high enough volume, this can devolve into a traffic jam, even if there is no theoretical loss of roadway supply. Once a road is congested, it requires a drop in demand to become less congested. That may not happen post-eclipse.

In most cases, we have a good idea of how traffic will behave. In urban areas, we see this occur on a daily basis. In more rural areas, there are certain locations which have frequent traffic when city-dwellers (and suburb-dwellers) return from weekend travel. In New England, these are somewhat illustrative:

  • I-95 southbound in New Hampshire traffic is the product of two merges and two sorts. First is the 95-16 merge, a 5-to-4 merge. Then is a sort-and-merge for the Hampton Tolls, which were inexplicably built with only two through lanes of toll booths even though 75% of weekend traffic pays electronically. As people move around and squeeze into these lanes, it causes severe congestion. From there you’d expect that the 4 lanes of traffic feeding into 6 (95 south and 495 south) wouldn’t be congested, but with the toll sorting, traffic then has to re-sort to the two destinations, causing additional congestion. (Northbound traffic, while usually not as bad, also has multiple merges and sorts.)
  • I-93 between Manchester and Concord. While the toll sort here is also problematic, the main issue is the 4-to-3 merge in both directions, with additional traffic streams joining. So again, a merge impacted by a sort.
  • The Cape Cod bridges. 3-to-2 merges, short merge distances, narrow lanes with poor sight lines, etc.
  • The Turnpike at Sturbridge. Eastbound it’s a pretty simple 4-to-3 merge. Outbound it’s theoretically 3-to-4 but the sorting into the exit to 84 often backs up miles. (The 290/395 exit often creates its own traffic jams, sometimes these merge: fun!)
  • I won’t get into Connecticut but the highways there seem to have been planned by looking at a bowl of spaghetti, with left entrances and exits and merges and sorts which will congest in a slight breeze.

Aside from these, and Connecticut, Providence and Boston, there’s just not a lot of traffic in New England. On some fall foliage days, a few single-lane roadways in New Hampshire can have backups of epic proportions, mostly when a town (or even traffic light) lies between a road and a highway: The Kanc, Route 100, Route 16. These are traffic jams that occur a few days per year; a few miles of highway bypass could reduce them, but there’s other reason to do so, especially when some people are going to “do the Kanc” and don’t mind if it takes 4 hours to look at the leaves.

Once these people high the highway, there’s enough capacity for them until they get to a bottleneck closer to home. So we don’t really know how traffic is going to behave with more people on the roads than ever before. We have a sleepy, low-volume subway station and a once-in-a-lifetime event … and we are all taking the escalator.

This is different than Phish: the Vermont traffic jam then was caused by muddy fields which couldn’t be used for parking, and a backup onto the interstate (a mile of traffic only has about 200 vehicles in it; so this was basically a 30-mile-long stationary queue of cars trying to get to a parking lot that didn’t exist, until everyone abandoned their cars and walked to the show). That was caused by everyone trying to get to a single point (that wound up having limited capacity). The eclipse covers thousands of square miles. Many people will get there with time to spare (given how booked-out hotels are, days in advance for some). But once it’s over, it’s over. It’s on a Monday. Everyone is going home. We’ll converge on the same roads. The usual bottlenecks in New Hampshire may see some traffic. But there are new ones further north which have never seen this much traffic.

Vermont doesn’t have many continual traffic counters. There’s one just south of Barre/Montpelier. Peak traffic there is about 1000 vehicles per hour on weekdays, and up to 1500 per hour during peak season (foliage, ski). This is significantly lower than the capacity of a two-lane roadway (3200 to 4000 per hour). The one near Waterbury is similar, there’s a bit more traffic right near Burlington at commute times. These roadways never operate at even 50% capacity. So we have very little idea how they will operate when at or over capacity, particularly when these flows hit downstream bottlenecks.

The AADT (average annual daily traffic) on I-89 ranges in the 20 to 30 thousand range, other area highways are far lower (in New Hampshire, I-93 has an AADT in Franconia Notch of 11,000, and under 7,000 a few miles north in Vermont). During peak summer and foliage weekends, I-91 in Vermont sees as many as 8000 vehicles per day. The busiest stretches of roadway in Boston see that many vehicles per hour in each direction. There are some expectations of 200,000 people going to Vermont for the eclipse. This is a week’s worth of traffic on I-91 and I-89.

So around 3:15 on Monday, or a few minutes after, we’re going to see all sorts of new bottlenecks and people flow onto highways for the trip south. Where will it be worst? Here are my predictions/guesses:

  • I-89 south of Burlington. Burlington traffic will fill the road, which then runs along the south side of the path of totality, so additional traffic in Waterbury and Montpelier will attempt to merge on; and this is a road with relatively high baseline traffic.
  • White River Junction. The ramps here are not designed for peak traffic traffic, although the likely peak demand (89S-91S and 91S-89S) luckily do not overlap.
  • RIP anyone attempting to get from Vermont to New York on Route 7, single lanes and traffic lights do not have particularly high throughput. 87 in New York may not be much better and I wonder what the ferry lines will look like (although it would be a great place to watch the eclipse).
  • Franconia Notch. I-93 looks like an Interstate, but was built to non-Interstate standards through Franconia Notch after various legal wrangling. With 10,000 vehicles per day, the single lane merge never really backs up. With most of the Boston area converging on it at the same time, well, I’ll be avoiding it.

We have some data to go off of from 2017, when there were similar traffic jams around a very similar event. I tweeted out some traffic photos, shown here are people headed out of major population centers (Atlanta and Charlotte) towards the eclipse. And here’s what happens when there’s road construction narrowing a two-lane road down to one (I think the state DOTs have the message this time, it’s also still the season of winter, not construction).

TRB wrote about it, as did some academic articles. There were traffic jams reported across the country, and locations which had high levels of traffic for hours before, and especially after the event. Here’s a GIF of Google Maps traffic. A lot of the worst traffic was reported in places like rural Kentucky, Idaho and Wyoming which for all intents and purposes do not have traffic.

The eclipse passed over Wyoming, but not Colorado. So tens if not hundreds of thousands of Coloradans headed up I-25 to find totality near Casper. There are very few highways in Wyoming, so traffic was funneled onto this singular roadway. Southbound traffic from Wyoming to Colorado jumped 10-fold once the event was over. Backups were reported for the entire rest of the day, and a 4 hour drive wound up taking 10. I-25 is somewhat unique in that there are no local roadways to shoulder some of the load, so while it may not be a direct corollary to Northern New England, this level of delay may not be out of the question. For the most part, reports found traffic was densest after the event.

The weather this year may also concentrate traffic. 2017’s eclipse was mostly in the clear, but this year is going to be mostly cloudy, with only Northern New England and a swath from southern Missouri to Indianapolis in the clear. Both of these share the characteristics that they are near large population centers not in totality: the Northeast Corridor for New England (and potentially parts of upstate New York) and Chicago and Saint Louis (and others), so add to that longer-distance eclipse fans fleeing Texas and Ohio and traffic may get even worse.

Tips for optimizing for traffic? Well, first optimize for visibility. This is a couple-times-in-a-lifetime event. Once you’ve done that, consider getting yourself near the eclipse center line but pointed in the direction you want to wind up. Then get ready for a long ride home. And once I’m home, yes, I’ll scrape some data and analyze it in this space. (I might throw in some Mass Pike Superbowl data, too.)

The construction crew on the Key Bridge saved lives. (Just not that many.)

There have been many, many people on the Internet and elsewhere who have talked about the “many” lives saved by the quick actions of several layers of responders this week to close the Key Bridge to traffic. I’ll pick on Yonah Freemark here (sorry, Yonah), but you can find any number of twitterers talking about how many lives were saved. This guy said “it could have been hundreds” in an otherwise informative interview. The New York Times story about the audio says it “likely saved lives” which, as I’ll explain, is probably better phrasing.

The bridge collapse occurred at 1:30 in the morning. There’s a pretty good chance that, had the mayday call not gone out and had the local authorities not intervened, there would have only been two vehicles on the bridge, or perhaps none. The presence of the construction crew, which was not able to evacuate the bridge, may have been the reason the response was so quick, since there were police vehicles nearby. This leads to two lessons and a thought:

  • Major bridges over busy shipping channels should have means to quickly stop traffic (perhaps even automated gates)
  • Construction crews on such bridges should have good communications and be prepared to quickly evacuate.

The thought is that people vastly overestimate the use of highways at very off-peak times of day. The MTA probably has better data from electronic tolling, but the most recent public traffic count for this bridge seems to be from 2019 (the user interface for Maryland’s traffic counts—like most such interfaces—leaves a lot to be desired). It includes an early Tuesday morning, so it’s probably good enough for a rough estimate. From that, we can find that somewhere around 180 vehicles cross the bridge per hour between 1 and 2 a.m., which would mean that at any given time, there would be approximately 3 vehicles on any given mile of roadway. Since the collapsed portion of the bridge is about 2/3 of a mile long, we would expect there to have been two vehicles on the bridge when it collapsed, right?

Well, kind of. We actually have tools for figuring this out. What’s that music? It … sounds like the entrance music for the Poisson Distribution! The Poisson Distribution is “a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event.” This is basically how traffic works. (It’s also, for example, how passengers arrive at a transit node.)

We can use the Poisson distribution to find the probability that n vehicles would have been on the collapsed portion of the bridge given the traffic levels. This gives the following:

n = 0: 14%
1: 27%
2: 27%
3: 18%
4: 9%
5: 4%
6: 1%
7 or more: 0.4%

So the modal outcome is (1 or 2) but there’s about the same chance of no cars on the bridge as four or more at that time of day. Given that vehicle occupancy overnight is likely not much more than 1, the number of lives saved by this specific chain of actions is likely in the range of zero to four. If you watch the video, you can see the number of cars on the bridge basically ranges between 0 and 3. As we’d expect. Statistics are fun!

That said, there’s a lot this leaves out. Additional vehicles on a bridge approach could have Thelma-and-Louised off the bridge without warning given driver inattentiveness (although “road” is a major detail). More importantly, having these policies in place means that had this occurred at a higher traffic time of day, it would have prevented a mass casualty event (although it seems like the presence of the work crew may have been part of the reason there were police officials nearby, so we may be very lucky this occurred at 1:30 a.m. and not 5:30 p.m.). Using the Poisson and the peak traffic of 2700 vehicles per hour, there would be a 96% chance of at least 20 vehicles on the span, a 45% chance of at least 30, and a 3% chance of at least 40. (Still, “Hundreds?” Well, Poisson does have a long tail but the probability of that would be quite small.)

Beyond that, there’s an outlier event where the bridge has a traffic jam and vehicles couldn’t clear the bridge with advanced notice. This is why, for example, in the Mont Blanc tunnel, which had a previous mass casualty event, has very specific rules about vehicle separation, and the Tobin Bridge in Boston is closed when an LNG tanker passes underneath. But this roadway had a low-enough traffic count and is far enough from bottlenecks that it’s likely very rare that traffic ever backed up onto the bridge.

There’s also an argument that the ROI for rebuilding the bridge isn’t there for 32,000 vehicles per day (again, thanks, Yonah). Some caveats there. 1) The bridge had $57 million in toll revenue in 2023 ($31 million cars, $26 million commercial vehicles). This is about 8% of the state’s toll revenues, and much of the traffic might move to other tolled facilities. But there would be an overall loss of revenue. 2) The bridge is a haz-mat route and with the other two routes through Baltimore in tunnels, haz-mat would have to detour around the Baltimore Beltway. 3) Would the State of Maryland be able to recover salvage damages from the ship owners and insurers if they chose not to rebuild the bridge? I don’t know, I’m not a lawyer. (Or, for that mattter, a bridge engineer.)

Will such a boat-on-bridge failure happen again? There’s no reason to think it won’t. Ships are getting bigger, and there are only a couple of dozen bridges of this magnitude over waterways with large ships in the country (San Diego, San Francisco and Portland on the West Coast; Houston, New Orleans and Tampa on the Gulf; Jacksonville, Charleston, Chesapeake Bay, Philadelphia, New York and Rhode Island on the Atlantic, plus potentially Boston, Portsmouth, the Penobscot and a couple of canals, although these have much less traffic). In a sense, it already has, and the new Sunshine Skyway has significant deflection infrastructure around it (we just didn’t learn from that disaster). Perhaps this will be a wake-up call to reinforce deflection around vulnerable bridge supports. In the shorter term, large bridge operators should consider having SOP both for bridge users and bridge workers in case of this sort of event.

Early rail designers were just guessing

Recently, Alon asked about the curvature of the MBTA’s Providence Line, which also hosts* Amtrak’s service and has about half of the high-speed rail line in the country. It’s also some of the oldest railroad in the world and the Canton Viaduct is quite possibly the oldest high-speed bridge in the world (barely high speed: 130 mph / 209 km/h), with the bridge dating to 1835 and the rest of the line to 1834. Why is it that the old B&P railroad is suitable for high-speed operation while other railroads are not? It probably is mostly due to luck.

(* “hosts” is a strong word here; the T owns the fee, Amtrak maintains and dispatches the infrastructure and charges the T for this, but the T used to charge Amtrak. This is a whole, uh, thing.)

The first major railroad in the US was in Baltimore, with the Baltimore and Ohio running west along the Patapsco River towards Harper’s Ferry. This route followed the river valley and had numerous sharp curves in the river valley in the 4 to 6 degree range. The railroad was also built on deep granite foundations, much like the Boston and Lowell, as engineers at the time thought that track would be unstable otherwise (it turns out they were dead wrong; track needs some tolerance to move around, which is why today it is mostly laid on ballast). Several other railroads sprang up, mostly from coastal cities, and over a year between 1834 and 1835, three such railroads opened out of Boston, to Providence, Lowell and Worcester.

At this time, when communication between cities took days and across the ocean took weeks or months, there wasn’t much standardization for this new technology. Nothing had moved faster than the speed of a horse up to this point in history, and all of the sudden, large pieces of equipment could move 30 or 40 miles per hour, or faster. No one knew that the rails needed cross ties and not granite support, and no one really seemed to know what kind of curves and grades would be allowable. So, it seems, they guessed.

A note on railway curve measurement. In the US, it is generally expressed in “degrees of curvature” which somewhat paradoxically means “how many degrees of a curve are covered over 100 feet.” (This is a decent shorthand to avoid having to figure out the radius of big circles.) If you think back to trigonometry, a curve has 360˚ in it, so a curve that covers one degree in 100 feet will cover 360˚ in 36,000 feet (about 7 miles) and have a radius of 5730 feet or 1746 meters (the rest of the world often uses curve radius in meters for this). A one degree curve is quite shallow and can support speeds of about 130 mph.

Now, do you use the arc or the chord for this measurement? Generally chords, because the calculations are easier than for arcs (not a lot of pocket calculators in 1832). Highways use arcs. For all but the sharpest curves, the difference is inconsequential. With most mainline railroad track less than 8˚, it doesn’t really matter (it is more of an issue for streetcar track, for instance, Tower 18 on the Chicago L has approximately 70ish degree curves, with an chord of 130′ and an arc of 150′, they use radii).

So the B&O had sharp curves. The Boston railroads were built with fewer, and each company seems to have chosen a standard of sorts. The Boston and Worcester, which had less money than the others for construction and built west through more difficult terrain, was built with a number of curves in the 3˚ to 4˚ range, and many 2˚ or more (so, not really a standard). The Lowell and Providence lines were different: they had greater resources and connected Boston to established mill towns. Railroads at the time didn’t know if they could climb any significant grade, so attempted to avoid hills (they still do). Without any rivers to follow, the B&P and B&L attempted to avoid the glacial hills between their cities and slalomed between them.

For the Boston and Lowell, 2˚ was the measuring stick. The railroad has a number of curves, and nearly all of them measure to almost exactly 2˚, good for about 80 mph (depending on cant deficiency), which is about what the railroad there runs today. I don’t have any definitive information on this, but every major curve on the railroad is just about 2˚, few are less, and none are more. Immediately past Lowell, where the railroad was extended not much later, there is a 5˚ curve: engineers found out trains could make that kind of curve and built it (oh, and there were some expensive factories and a big river in the way).

Providence is similar: it, too, has to run between a number of hills on its way to Providence. The first 10 miles split hills in Boston and then follow the Neponset River, but the river only goes so far and the railroad eventually has to climb. The solution was a grade up to Canton, a bridge across the Canton River (a stream feeding the Neponset) and eventually a straight line from Mansfield to East Providence. The route to Mansfield has a number of curves, including across the Canton Viaduct. Measuring each, they all almost exactly 1˚, a speed good for about 130 mph.

This is the speed the line runs today. While not the highest of high speeds, it means that a trip from Back Bay Station to Providence, a route of 43 miles, takes 30 minutes, including a stop at Route 128 station; without that stop, the average start-to-stop speed would top 100 mph. This also includes the last few miles into Providence, which were built once the B&P realized that sharper curves were possible, so it was built with sharper curves.

The original Providence Station was east of the city, along the Seekonk River. This was suboptimally located for access to the city, and especially for through service (although a now-abandoned tunnel was built in 1909 and could conceivably provide a 3- to 4-minute faster trip between Boston Providence if the right-of-way in the city had not been realigned). In 1847, when the B&P built a connection to the Providence and Worcester railroad to a better location in the city, the connection to the main line was built a sharper curve—approximately 1.25˚—requiring trains there to slow from 150 to 110 mph today. The curvature is still sharper in Providence itself; until they reach the state line the speed limit is 70.

There are not many legacy rail lines which allow for high speed operation, certainly outside of very flat areas. Railroads want to avoid hills and before high speed operations they were generally built to go around them rather than over or under. Pretty quickly (or in the case of the B&O, very quickly) engineers realized that a 3˚ or 4˚ curve was perfectly fine, especially with stronger rails. No one in 1840 was going 100 mph, it was inconceivably fast. A few 5˚ curves were far easier than moving mountains.

But the Providence Line, because of—as far as I can tell—little more than happenstance, wound up with a high-speed right of way. It will never have 180 mph / 300 km/h service on those curves, and smoothing them out, especially at the Canton Viaduct, is nearly impossible. (The median of I-95 would give a straight-enough corridor for a higher-speed alignment to Providence, which would shave only 2 to 3 minutes off travel times but would allow for more redundancy and capacity.) But for a 190-year-old railroad, it’s not bad. It’s a shame engineers figured out so quickly that 1˚ curves weren’t necessary or we could have much faster rail service much more easily.

Note: here is a tool I created to find the curvature of rights-of-way, and no, I definitely didn’t write this post just to call attention to it. Not entirely, anyway.

Big event logistics and Taylor Swift

Or … the case for a stadium-specific train station in Foxboro instead of a sea of parking.

Football stadiums are big, but where do they “belong”?

Football stadiums are generally unlike other types of stadiums. With a few notable exceptions, baseball parks and hockey/basketball arenas are located in relatively urban areas. While they are sometimes surrounded by parking lots (ahem, Chicago) there is usually (but not always, looking especially at you, LA) relatively good transit access. Baseball stadiums generally seat around 40,000 people and are used for 80 to 90 games per year (plus other events), arenas seat fewer than 20,000 but a basketball-football-event arena may be used more than 150 times per year.

Football stadiums are much larger (generally 60,000 to 90,000) but far less frequently used. Aside from 10 or 11 football games, even a large city may only attract a few acts which can fill a 70,000 seat stadium: the Taylor Swifts and Bruce Springsteens and Beyonces of the world. MetLife Stadium in New York has just 23 large events aside from football this year, meaning it sits idle more than 300 days of the year, and it is likely the most heavily-used stadium in the country. There are only a few stadium-level acts touring at any time (it’s a lot easier to fill a 20,000 seat arena compared with a 80,000 seat stadium) and outdoor events can really only take place between May and October in most places. A large stadium will be a ghost town most of the time, not a great land use if you’re trying to build a vibrant area around it.

A ballpark or arena may see upwards of 4 million visitors per year, spread over 100 dates or more. Football stadiums may barely crack one million, concentrated into a couple of dozen dates. These two factors mean that these large stadiums are often sited differently than smaller arenas in the US. But when nearly 100,000 people descend on one location, it’s not easy to accommodate them. Football stadiums can leverage existing downtown infrastructure (transit and parking) but this can lead to or exacerbate to poor surrounding land use. Or they can be built in another existing, American amenity: the suburbs.

A quick aside: American like our stadiums like we like our highways: big. Of the 11 stadiums with a capacity over 100,000, eight are in the US (all college football, two of the other three are cricket, the third is in North Korea so who knows how big it actually is). NFL stadiums are usually a bit smaller, with more premium seating. Still, they’re big, Americans drive cars a lot, and football fans like to stand outside their cars and eat food and drink beer before the game so with few exceptions, at least some outdoor parking is present.

As Ray Delahanty recently pointed out, it’s tricky to get good land use with that size of an arena if it’s placed near a downtown. I’d go further: in the United States, football stadiums are so big and so car-focused and lightly used they don’t belong downtown at all. There are large stadiums in non-US cities which manage to avoid parking seas, although in general they are located in cities where the majority of people don’t drive (don’t worry, they still drink before the game). Of stadiums larger than Soldier Field, the smallest NFL stadium (62,000 seats), 70 of 153 are in the US, including 29 NFL stadiums and plenty of other college stadiums. (Other countries with at least 3 on this list: UK with 7, Germany and China with 5, Brazil with 4, Japan, Mexico, India and Spain with 3, often with access to multiple metro lines or near a major railroad station.) So midsize metro areas and college towns in the US have larger stadiums than the national stadiums in most countries.

Because of these factors (big, America, cars), football stadiums have developed with a lot of parking. The actual football field of play covers 57600 square feet, or about 1.3 acres (wider soccer fields are about 77,000 square feet). The stadium surrounding the field might take up around half a million square feet, or 10 times more. The parking around a football stadium? It takes 10 million square feet (in some cases, more), about 230 acres, which is worth point out is more than about a square kilometer, or nearly 20 times as much space as the stadium and 200 times as much as the field itself.

Many stadiums are indeed surrounded by this sort of sea of parking. Professional American football stadiums tend to fall into two broad categories: those in the suburbs and those downtown. (Larger college stadiums are often much less parking-dependent: many fans come from the adjacent campus and weekend games utilize campus employee parking which otherwise sits empty). Suburban stadiums are generally parking seas: in nearly all cases they utilize stadium-specific parking. (The two exceptions are in Green Bay, when neighborhood streets, yards and lawns soak up much of the parking demand, and Santa Clara, where nearby office parks can be used for weekend events.)

Urban stadiums are rarely islands in the middle of parking seas. For the most case, they rely on existing parking facilities in the downtown neighborhoods they border. There are two glaring exceptions, both of which somewhat paradoxically date back to the early 1900s:

  • Denver’s Mile High Stadium (or whatever it is called now) is urban-ish. It’s a bit more than a mile from Union Station and the edge of Downtown, too far to take advantage of Downtown parking garages, although there are some closer transit connections. It was originally built on land that existed because it was an early-20th century landfill.
  • The South Philadelphia Sports Complex, which dates to filled river delta area in the 1920s. The original purpose of the land was to build a large arena for the Army-Navy game larger than the ballparks which football fields were typically squeezed into at the time. This led to perhaps the most robust stadium-only transit service in history. Since neither team was local (the game taking place roughly in between Annapolis and West Point), the Pennsylvania Railroad ran dozens of special trains to a temporary station built on a rail yard adjacent to the stadium, handling tens of thousands of cadets, midshipmen and other attendees. The extension of the Broad Street subway line wouldn’t be built until the 1970s.
Grif Teller’s “Mass Transportation” depicting the Army-Navy game trains.

No modern stadium has been built near a city center with a full 10-million-acre parking ocean. Even here the economics don’t work to have massive parking lots only used a few days per year. It makes much more sense to utilize nearby parking garages which are usually empty on Sundays and that’s what generally occurs. There is some space for tailgaters, but most event-goers use parking garages. An added benefit: downtown areas are designed (for better or worse) to accommodate a lot of people arriving by car at the same time, and usually has a decent transit system which can bring in a fair number of event-goers as well. It’s interesting that there are a number of cities with NFL stadiums and no appreciable rail service: Las Vegas, Jacksonville, Charlotte, New Orleans, Detroit, Indianapolis, Nashville and Cincinnati, and only Atlanta really has a heavy rail-served downtown stadium

Moving a lot of people to one location is … hard, actually?

While these stadiums are at the center of urban bus networks, bringing tens of thousands of people to one place on buses is difficult (for instance, loading 20,000+ people onto buses for the Boston Marathon requires closing several blocks of streets to stage buses and to load them in two lanes at a time, a large queueing area, and all this for a single origin-destination pair, so there is no need to direct people anywhere than to “get on any bus”). And even if these smaller cities took advantage of their bus systems, they would be quickly overwhelmed. Nashville’s system only operates 150 buses at peak times, and only carried 11,000 people all day on Sundays before the pandemic. (Indianapolis, Jacksonville and Cincinnati operate on a similar scale, and several other cities’ transit systems aren’t much larger.) Even if buses were used at scale, it would require a huge fleet. At 50 people per bus (meaning selling almost exactly 100% of the seats on a bus, not an easy task), transporting 20,000 people would require 400 buses, plus dispatch staff, crowd control and route planning. This would dwarf the bus fleets of smaller cities, and since the buses would only provide a single round trip, it would require a full shift of bus and driver pay to move a single load of people, not a particularly efficient use of resources.

Picking up a lot of people in one place and moving them to another happens to a task at which mainline commuter trains excel. A 10-car train can carry upwards of 2000 people (more if packed with standees), so even if one third of attendees came by transit (unlikely for a football game, but more likely for, say, a concert for a singer popular with teens and 20-somethings) it would only take 10 trains to transport everyone. Trains could also transport event-goers to park-and-ride lots unused at off-peak times. 10 trains might only require 50 staff, an order of magnitude less than buses to move the same number of people.

Football stadiums are not designed with transit in mind. There are three football stadiums for which commuter rail is the only high capacity transit connection (others—Baltimore, Seattle, Santa Clara, Chicago’s current stadium—have rail lines nearby but more heavily utilize other forms of transit): the Meadowlands in New Jersey, Foxboro outside of Boston and the proposed Arlington Park stadium outside of Chicago. Not surprisingly, these are the three most extensive commuter rail networks, and in each case, the rail connection is made far outside the city. Each city provides an interesting example of how commuter rail service does, or does not, provide transit access to large events.

Chicago (Arlington Park)

Chicago doesn’t have a football stadium served by commuter rail, yet, but it may not far in the future. The Bears are planning to move from the smallest-in-the-league, 100-year-old Soldier Field on the periphery of Downtown to a larger, more modern suburban stadium on the site of an old racetrack. It’s hard to fault them for this: a new stadium downtown or anywhere near transit would require a large site that would only be used a few times per year. (I guess adjacent to the United Center or Comiskey would work?) Arlington Park is about 20 million square feet (nearly a square mile, three times the size of Suffolk Downs in East Boston) and adjacent to a three-track commuter railroad, which can support frequent service and a 30 minute ride into the city (it also runs on a diagonal through the Northwest side of Chicago, with a number of stations allowing bus and L connections).

Unlike some agencies, Metra is actually pretty good at running extra service to meet extra demand, and would likely be able to stage as many trains as were necessary to move people from this new arena to the city, and also to satellite commuter parking lots along the line. The third track of the railroad would allow the agency to stage as many trains as necessary to handle crowds while maintaining regular service. The station has two adjacent storage tracks, and a new development could allow for an expanded station to manage higher loads. The Bears’ plans don’t call for a sea of parking, but rather a mixed-use development next to a train station. Would I call it a perfect location? I might not go that far, but it’s a decent place for a 75,000-seat football arena.

New York (New Jersey Meadowlands)

Both the Jets and Giants play in the Meadowlands, build on reclaimed land in the swamps in New Jersey. The shared use of of the stadium means that it gets somewhat more frequent use than it otherwise would (a low bar; it still lies dormant more than 300 days each year), and with many non-drivers in the area a rail spur was eventually built to take people to and from the stadium. (It only cost $185 million—equivalent to $265 million today—for 2.3 miles. Really. It may serve 500,000 people per year, or about 1500 per day on average. And it may not even be the biggest boondoggle in the Meadowlands.) Other than events, there is no use of the line, which only serves the sports arena and the American Dream shopping mall, which opened after a 25-year, on-and-off construction period and may be all but stillborn, hemorrhaging money now that it has finally opened its doors (i.e., boondoggle). For football games, it works fine, with between 6000 and 10,000 people arriving and departing by train. For larger events, like line has been overwhelmed since the stated capacity of the line is just 8000 to 10,000 per hour.

This speaks to a bottleneck somewhere along the line:

  • Perhaps it is an undersized station, with just three tracks (the rail station at Belmont Park on Long Island was originally built with eight tracks, although only two are now in regular operation). 8000 to 10,000 people per hour means that the rail line only supports a full train every 12 to 15 minutes, which hardly seems like the capacity of the line. With three tracks, the Meadowlands station should be able to turn a train in 15 to 20 minutes on each track (and that’s generous, since trains are only loading or unloading at any given time passenger traffic flows in one direction) meaning that the station should support 9 to 12 trains per hour.
  • Maybe line capacity? The upper bound of the station may stretch the capacity of a two-track railroad with diesel trains and an intermediate stop and existing service; the 18-track terminal at Hoboken would be able to swallow the traffic at the other end of the line. The Pascack Valley, Bergen and Main Lines, which share a trunk route into Hoboken, only amount to three trains per hour at off-peak times (when nearly all concerts and events end, either on a weekend or late in the evening). These lines support 12 trains per hour through Secaucus and into Hoboken at peak hour, meaning that 9 stadium trains plus the normal service would be reasonable. That should allow 18,000 people per hour to be moved.
  • My guess is that it’s simply the number of trains on the line for high-use events, and inexperience of the agency. With a cycle time to Hoboken and back of more than an hour, NJT would have needed more than a dozen trains on the line to fill the theoretical capacity of the line and station, so rather than having trains stacked up on the line ready to pull into the station, they were relying on six trains to make the round trip and come back for more. This is certainly better for crew utilization, but not so great for the passenger experience.

The 2014 Superbowl, where fans were highly encouraged to take transit, was a stress test the railroad seems to have failed somewhat spectacularly. It took three hours to clear 35,000 people from the stadium; 12,000 per hour is actually higher than the stated capacity (likely as people pushed onto trains) although some very helpful Internet people suggested just running buses without pointing out that they would have needed about 700 of them. If I had to guess, the issue was a lack of trains and crews:

Boston (Foxboro[ugh])

Which brings us to Foxboro, the third stadium near a commuter rail line. Sort of. There hasn’t been regular passenger service on the Framingham Secondary since 1933. 40 years later, the stadium itself was built, on a shoestring $7 million budget on donated land. At the center of this land deal: parking. The league stipulated that teams play in 60,000-seat stadiums. The itinerant Patriots had used a number of smaller venues: Fenway Park, and three small college stadiums (Harvard, BU and BC) and unlike the Bears, which moved from Wrigley to a “temporary” home at Soldier Field (they’re now looking to move half a century later), there was no large-enough structure in the area.

The owner of a local racetrack offered the land for the stadium but kept the adjacent parking lots which would now generate cash for both horse races and football games. The site happened to be adjacent to a rail line, and from early on some event service was provided. Service, however, is minimal, since the rail line isn’t designed for much more than a few freight trains. In general there is one train from Boston and one from Providence (the Boston train usually sells out) which meet at the platform. There’s no room for anything more. Aside from the poor local infrastructure, the railroad could support direct service from Boston, Providence and Worcester, theoretically linking the stadium to the three largest cities in New England, provided there was room to store more than two trains.

In the past 50 years, Foxboro’s sea of parking has grown, as the complex owner Bob Kraft has since developed a large shopping mall adjacent to the stadium (more of a lifestyle center than the atrocity that is the American Dream in Jersey). This is not a good setup for traffic as Foxboro is accessed by Route 1, a four-lane highway with traffic signals, and traffic is notoriously bad after games (one review calls it a “great stadium with terrible traffic,” a microcosm of Boston, depending on your definition of “great”). Lots of advice to beat the traffic is to take the train, although it means no tailgating and capacity is limited.

Most everyone else has to drive. There are two ways to distribute a lot of vehicles parked in one place. One is to surround the parking lots with highways and ramps (either in the suburbs or downtown). Another is to disperse parking near the stadium, allowing it to filter through nearby neighborhoods (Green Bay does this, but no one in Green Bay complains about Lambeau Field, which is probably against several state laws). Foxboro is located in the corner of a far-flung suburb a quarter the size of the stadium’s capacity. Decisions are made by an open town meeting. The stadium is located on a local four-lane roadway with traffic lights before it spills onto nearby highways. Traffic jams are legendary.

In 2019 the MBTA started, then aborted with the pandemic, and now restarted, a yearlong pilot to bring regular service to Foxboro, partially subsidized by Patriots ownership. Parking is provided for free, which may help apparent ridership, but there’s really little other reason for most riders to go to Foxboro instead of another nearby station, especially since rush hour service from nearby Mansfield is a faster trip by 20 minutes. (Before the pandemic, other lots would be full, but even with ridership bouncing back, parking scarcity is not as much of an issue.) With nothing but parking lots for a mile in any direction, there is about as much need for transit service to the site as there is to a mall Jersey. High ridership, for now is little more than an American Dream.

A station for Foxboro (and Tay Tay and … the World Cup?)

Which is not to say there shouldn’t be a station there. It should, if the 12 million (half square mile) of land were ever developed as something other than parking lots. It may be the largest developable plot of fully-impacted land in the region. And it happens to be next to a railroad. So while the current pilot may not be successful, if the surrounding area were home to 5,000 housing units it would make far more: Windsor Gardens, but on steroids, an anchor a the end of the line. I’m sure the citizens of Foxboro, who enjoy the largesse of the stadium’s tax revenue while keeping the traffic on Route 1 on the periphery of town, would throw a fit, but in Boston right now, nearly any housing is good housing. Transit-oriented? Even better. (In the very long run, a shuttle train to a connecting service on the higher-speed Providence Line might make more sense.)

In the short run, however, the line is wholly inadequate for handling crowds: it consists of one long platform which can handle, at most, two trains, and the slow, single-track lines in either direction make it nearly impossible to store or stage additional equipment near the stadium. So once a train is sold out, it’s sold out. For Patriots games, there’s not too much demand past what is provided. But when a different demographic comes to town, the situation can get dicier.

Enter Taylor Swift. The only ticket hotter than a T Swift ticket to Foxboro was a ticket on a train to get there. Rather than the SUV-driving, tailgating, suburban type, Swifties seemed happy to snag a seat on Commuter Rail from Boston, such that the first batch of tickets sold out almost instantaneously, and when more were added, they went in 90 seconds. (The Swifties who did get onboard seemed to enjoy themselves!)

The lack of any terminal facilities in Foxboro means that there is no way to leverage the existing rail line to bring crowds to the site and reduce the need for parking, parking which could be repurposed for something other than a parking lot only used a few times per year. There is plenty of room for an event rail terminal not significantly different (although at a smaller scale, sketch here) from what the Pennsy ran for the Army-Navy game, in essence, a few tracks facing in each direction allowing trains to park and unload passengers before the game and then swallowing them up afterwards. It need not be fancy, just ramps to platforms to allow accessible boarding for trains waiting for the crowds.

This would allow multiple trains for football games, where there is more demand than current supply and plenty of capacity at nearby park-and-rides at game times. An express train could run from Boston with a local train picking up passengers parking at nearby stations and using the train to avoid the last few miles of gridlock. For an event like a Taylor Swift concert, as many trains as needed to transport the requisite masses. Full trains make money. If the Cape Flyer makes a profit on an $40, 160-mile, 5 hour roundtrip with a couple hundred passengers, 1800 people on a $20, 60 mile roundtrip should be a cash cow. The agency has the resources at off-peak times, and events are scheduled far enough in advance that labor could be arranged well ahead of time. But the real value is in repurposing the land around the stadium from parking to something more beneficial to the region.

It’s hard right now to make an argument that the current Foxboro Stadium land use needs regular transit service. In a region with a housing shortage and relatively few large sites adjacent to rail lines, the half square mile of parking could be put to far better use if it weren’t needed and there was enough transit service to allow people to get to the stadium without driving (even if it just meant parking at an existing Commuter Rail lot elsewhere and taking a train). Should the public pay for this? Certainly not. But if improved rail service were funded by Bob Kraft, it would be a good investment which could leverage the value of the acreage around the stadium to be something other than parking cars for a few days each year.

In the shorter term, Foxboro will host at least 6 games of the 2026 World Cup. These fans will be much closer in demographic to a T Swift concert (international, interested in soccer, less interesting in tailgating) and many will be staying in hotels in Boston (and probably Providence, too). If the T can’t figure out how to manage moving more than 3000 people to and from the stadium on trains, they’ll have to have a fleet of buses, and all of the logistics that go with that. So if there is a good time to build a stadium terminal which can handle larger crowds that time is now.

Queuing theory, inefficient Search Algorithms (or … where’s my bag at the Boston Marathon?)

I’ve run the Boston Marathon five times now, and during three of those, I’ve waited for my bag in a cold rain at the end of the race. While this is certainly preferable to the alternative, the marathon’s bag pick-up illustrates how systems can experience bottlenecks even if the overall system has plenty of capacity.

Boston is a unique race in many ways, but because it requires qualification for most runners, it is perhaps the most “densely-populated” marathon in the world: rather than spreading finishers across a four hour window (2 to 6+ hours), most are concentrated in the qualifying window (under 5 hours, depending on age, with most runners under 4). It certainly isn’t the largest race: New York, London, Paris, Berlin and Chicago all clock in around 50,000 runners, while Boston has settled in at a maximum size of 30,000.

The reason that Boston is smaller is that unlike those other races, it starts in a small town, takes over the high school for the athletes village, and the first few miles are on a two-lane wide road with no shoulders, meaning that even spread across four distinct waves, there are only so many people who can be bused to the start of the race, lined up, and started. (Chicago, by contrast, starts and ends in the Loop, Berlin, London and Paris are served by massive transit systems and New York uses an armada of buses to move people a couple of miles from the ferry to the start, which happens to be on to a major highway). On race morning, the parking lot behind the Hopkinton CVS is a sea of port-o-johns; New York uses the 160-acre Fort Wadsworth, Chicago starts in the middle of Grant Park.

(Aside: as I stood in line for the line for mobile urinals—a Nobel-worthy invention in the field of race waste management—people next to me worried we’d miss the start. “Nonsense,” I said, doing some quick math. “There are 80 urinals. There are about 250 people ahead of us in line. If each person takes 1 minute, we’ll be done peeing in 4 minutes.” We were. Logistically, each urinal holds about 400 liters and men can pee 10 to 20 ml/sec per the Internet, so these urinals will not fill up during the 90 minute pre-race pee period. Let’s move on.)

The roads in Boston eventually widen, although most of the course is less than four lanes wide. When you take this relatively narrow course (parts of London are narrow as well), and add, unlike the other races, the seeding of qualified runners, it means that the field never spreads out. Marathon finish times mostly resemble a bell curve (although with some eccentricities, discussed momentarily). The “average” marathon has a median time of about 4:30 with a standard deviation of about an hour. Boston has a median of about 3:45, with a standard deviation of only about 40 minutes. (Standard deviation data can be found here; European races tend to be a bit faster than American races on the whole per the study linked below.)

Why is it not an exact bell curve? Because many runners attempt to—and generally succeed in running—specific times. [2:59:56 marathoner this year raises hand.] Here is a very interesting business school paper on reference-dependent preferences which included the results from several thousand marathons and shows the distribution of marathon finish times.

Distribution of Marathon Finishing Times (n 9,789,093) 

The n in this study is 9,789,043, so 100,000 finishers is just about 1% of the race, and other than a peak right around 4 hours, most of the race is under 0.8% per minute. Boston, on the other hand, has a solid hour with more than 0.8% of the race finishing, with a peak minute of 1.4% or 372 runners (in 2023) and several other minutes around 1.2%, or about 320 runners per minute. And that peak reference-dependent preference is a full hour earlier.

In other words, in a typical marathon, 40% of the runners finish in the peak hour (between about 3:35 and 4:35). In Boston, 60% of runners finish in the peak hour (between 2:55 and 3:55). 40% of runners finish across just 38 minutes, a rate more than 50% higher than typical.

Add to this: Boston’s runners are very well-seeded, so the heavy waves tend to start and finish together. In nearly every large race, runners are sorted into waves to start, with each wave starting every 25 to 35 minutes (rather than having one huge field stage and take 30+ minutes to clear the start). In larger races, the wave start means that although there is a peak between 3:55 and 4:00, that peak finishers are spread across multiple start waves. Most runners near the peak in those races do not have a qualifying race time, and are seeded based on interpolated times from other races.

Meanwhile, in Boston, the first three waves of runners almost all have qualifying times based on a recent marathon and are seeded quite well. Boston has less of a reference-dependent preference signature other than at the 3:00 mark, which happens to be the qualifying time for men under 35 and a significant goal for many runners. In fact, the largest single race for people qualifying for the Boston Marathon is usually the previous year’s Boston Marathon (the only exceptions are when the weather is uncooperatively warm). So in other races, at the peak times, runners are spread across multiple waves (not finishing all together), while in Boston most runners coming in at peak times started together (and in some cases ran the whole race within earshot).

Note: I could go and scrape start and finish data with gun times to go into this further, but for now, just trust me on “Boston has a lot of runners finishing together.”

Data from here. A few notes: the BQ standard was decreased by 5 minutes for the 2013 and 2020 races. 2004 and 2012 were run with temperatures in the 80s; 2012 allowed deferrals. 2013 was cut short because of the bombings, but at that point nearly all potential qualifiers had finished; 2014’s field was larger and consisted of many people who hadn’t finished in 2013; most were not qualfiers. 2016 and 2021 were relatively warm years. With 13,700 BQs run, 2023 Boston is the largest number of Boston Qualifying times ever run in a single race. This will likely mean that, after two years where all qualified runners gained entry to the race, there will be a cutoff in 2024.

This all means that at peak finishing times, there are not only 1000 people finishing per minute, but for much of the race, those people all started together. And what does this mean for bag pick-up? Here’s how bag drop works:

  • Before the 2013 attack, Boston had bag drop at the start: you gave a volunteer your bag and it showed up in Boston on a bus a few hours later. (See DC Rainmaker’s blog post, back before he started reviewing every device.)
  • After 2013, a bag drop policy was instituted at the start: you left your bag there and took a disposable bag to the start (and for cold years, wore extra clothing, transferring throw-away items from the Goodwills in Boston to Hopkinton).
  • Setting up a bag drop system for 20,000 or more bags requires erecting the infrastructure in Back Bay the day of the race; at first, this was tents and rows of bins with bags, the system has now morphed into one where you drop your bag at a school bus where it is stored through a window specified by your number range, allowing the storage units to be rolled away after the race (this, on its own, is a very good idea, here’s an image which shows how the easy part—the drop-off—works).

However, the system is still quite space-limited. Most every other big marathon ends in a park, or open area. Boston ends on a main street in the middle of a city. So there is not much room for queuing or storage for the bag drop. Which means that each bus stores approximately 1000 runners’ bags. Which is fine when they are dropped off: runners arrive over the course of about an hour per wave, with some early birds and some late arrivals, meaning about 15 drop-offs per minute, and drop-offs do not have to be sorted to the right person, only put into the right “bin” (a window of a school bus and on the inside, I assume, a numbered seat).

The buses are lined up by wave (red, white, blue, yellow) and then bags are ordered within each wave (1-1000, 1001-2000, etc). It is easy for race volunteers to look at a runner’s bib color and send them in the right direction to drop off their bag. They do, and go off to run their race.

On the pickup end, however, metrics are reversed. 1000 runners may show up over three minutes, and I’d guess as many as 600 of them may all need to get their gear from the same bus. Simply throwing random bags to runners would require, at times, more than three bags per second to be thrown at participants. But unlike drop-off, pickup requires sorting through as many as 25 bags (assuming a bus has 30 seats and bags are sorted into these seats). Without perfect ordering, volunteers search through the pile of bags until they retrieve the correct one. This may take 10 to 20 seconds or more, and even with five or ten volunteers on the bus (there really isn’t space for more), it means only 15 to 60 participants receive their bag each minute. If we assume the geometric mean here of 30 runners served per minute, it would take 30 minutes to serve all the bags in a bus, resulting in long queues.

As this occurs, a wave of long queues forms. Once the high rate of finishers starts around 2:50 from the start, the buses have long lines which form a slow-moving wave from bus to bus. After waiting for my bag in the 4000s for a long period of time in the cold rain (as I have in 2015 and 2018) I shuffled past the bus ahead of me with the 3000s. Aside from a few stragglers, it had no queue, the volunteers there had retrieved all of the bags and were catching their breath. Meanwhile, the queue behind me at the 4000s bus was ebbing, while the queue at the 5000s bus behind us had grown. But elsewhere, three-quarters of the buses, for the white, blue and yellow waves, wouldn’t see their first runners for, in some cases, an hour or more.

In introductory computer science courses, students are often taught about efficient search algorithms. Let me stop here and state that I am completely unqualified to write in depth about the efficiency of search algorithms. But mostly, it is very inefficient to search through an entire unordered list each time you want to find an item. It’s better to either sort the list (and then search through it) or sort the search term in a way that only searches part of the list. (That said, this is, let’s just say, a simplification, people write dissertations about this.)

Essentially, searching an unordered list is what the pile of bags search is. One solution would be to build a better sorting apparatus: I have participated in the American Birkebeiner ski race every year since 2006, and even produce the most popular (read: only) podcast about the race. Drop bags there are sorted and lined up, by number, in a parking lot, and distributed to finishers. This would work in Boston, if only there were several acres of parking lots in the Back Bay which could be used to stage the bags. Fortunately, urban renewal mostly steered clear of Boylston Street (the Pru was built mostly on old rail yards) and we lack the luxury of this open space. The school bus solution allows the apparatus to be set up on the streets, while providing cover from the weather for the bags (and volunteers), but does not lend itself to sorting beyond these bins.

If finishers were better distributed amongst the two dozen (or so) buses as they crossed the line, the sorting problem would be less of an issue. If 240 of 300 people crossing the finish line each minute had dropped a bag and they were evenly distributed amongst the buses, it would mean 10 people per bus per minute, and if five volunteers were on each bus, it would allow 30 seconds per bag for each user without long queues forming. The issue is that with this inefficient search algorithm—which is necessitated by the location of the bag pickup—has concentrated finishers. Hundreds of finishers wind up at a single bus at any time, and there are only so many volunteers who fit on this bus. When these “servers” can’t keep up with the demand of the “customers” (to use queuing theory terminology), the queue grows exponentially until, at some point, the wave of runners ebbs, and the speed at which customers are served exceeds the additions to the queue, and the lines dissipate. Of course, by this time, a similar wave has moved to the next bus down the line.

The author’s 2023 drop bag. Note that this bag (or at least, the 2022 version) can hold a 30-rack of beer (not pictured). No word on whether anyone has ever dropped off a 30-rack.

There is, I believe, a solution to this problem: sort the customers before they get to the bags. The main issue with this setup comes from a concentrated wave of people overwhelming a single service point. If the people were dispersed to more servers, it would allow more efficient use of the volunteers, rather than having one bus overrun while others lie idle. There is a simple way to do this: sort first by the last digit of the bib, and then by bib color and number. This would decrease the concentration of the customers by an order of magnitude, distributing them across the buses, rather than having them queue up in one place where there aren’t enough volunteers to handle them.

Here’s how such a system could work. When the BAA gives out drop bags, runners affix a sticker with their number and wave color. For instance, it might say:

4 8 7 6 or 1 8 7 6 5

This allows a rough sort by color and then number, but color is simply a function of the number, so it does not spread out the customers. Here’s a proposed redesign:

4 8 7 6 or 1 8 7 6 5

What I’ve shown here is that the numbers could have the final number highlighted to help inform people of the new sorting method, allowing the runners to be sorted first by the final number of their bib, and then ordered by their number. This would reduce the concentration by a factor of 10.

Directions about the changes could be given to runners with their drop bag sticker, as well as at the bag drop-off in the morning. Instead of signs pointing to different colors, they would instead point to numbers: 0 to 3 to the left, 4 to 6 to the right, 7 to 9 straight ahead. The start would be less tricky: before the race, people are generally more mentally aware than after running 26.2 miles. Once overcoming this small hurdle, runners would proceed to their number, then to the bus assigned to their color (each bus would likely have two waves assigned) and then the correct range. It would introduce an extra sorting step at the start, but would pay dividends later on.

The finish would introduce more complexity: runners and volunteers would have to direct people based on the last number of their race bib. This would be mitigated in a couple of ways. First, racers would have already experienced the system before the race. Second, volunteers already have to sort barely-cogent runners stumbling their way along Boylston Street by color, so they would instead sort “right/straight/left” by bib number. Once on the right street, runners would be able to find their correct bus by last digit and then color and join a much shorter and congested queue. Rather than 15 to 30 minute queues for bags, most runners would be served in just a few moments.

It might also allow the race organization to cut down on number of volunteers required for the system. Rather than moving volunteers between buses as demand changes, each bus would have even demand during the entire bib pick-up procedure. This would reduce “deadhead” time when volunteers are required to move between buses as they are needed elsewhere, by allowing them to maintain a single duty station during the entirety of the bag pickup process. There would still be 300 or more finishers per minute, but they would be spread across 10 pickup locations at any given time, not concentrated at a single site.

Since this is sometimes a transportation-related site, there is a lesson here in the transportation planning realm: A system which seems efficient may have an unforeseen bottleneck which creates a single point of failure, meaning that a small portion of the system is oversubscribed while the rest is underutilized. A wide highway might encounter a lane drop or even a situation where traffic has to sort into different lanes, resulting in a long backup. A rail line may have plenty of capacity along most of the line but a busy station with long dwell times or a single switch may curtail capacity along the rest of the line. For the Boston Marathon bag pick-up, the well-intentioned decision to simplify the drop bag system results in a bottleneck of hundreds of cold runners huddling under thermal sheets, all too often in cold rain. Simply by changing some procedures, this may have a fix which would benefit everyone involved.

Fixed guideway utilization

I’ve been part of the calls for the transformation of the MBTA’s Commuter Rail network to more of a “regional rail” network, with more frequent service, especially at off-peak times, for quite a while. The agency has been taking some very small steps towards regional rail, most notably by increasing frequencies on most lines to hourly (where, before the pandemic, midday ridership had been every two hours in many cases, and sometimes worse), and improving service on some lines on weekends (where trains in the past ran only every three hours in some cases). This had led to relatively strong ridership, despite less rush hour commuting, with reported ridership at 76% of pre-pandemic levels. (A caveat is that unlike an agency like, say, Metra, the T has not released much public data about commuter rail ridership.)

There are few “legacy” commuter rail networks in the United States, which have had service dating back to privately-run commuter service (generally in the 1800s). A short history of commuter rail (I’ll defer to Sandy Johnston for the definitive history and yes, you should read his history) is that it is almost as old as the railroad itself, with the first “commutation” fare (a reduced fare for frequent riders) showing up in 1843 in on the Boston and Worcester Railroad. Commuters became an important service and income source in certain large cities, although not in all; in many cases, interurbans or streetcars provided longer-distance services (although often with more frequency than commuter rail). For instance, Los Angeles had no historic commuter rail service, but the Southern Pacific-controlled Red Cars provided a similar service (as did the Key System in the Bay Area and even, to some extent, “Speedrail” in Milwaukee).

In the early 1950s, ridership grew as the suburbs grew, but began to quickly decline as the already worn-out physical plants deteriorated further and the services began to lose money, especially as jobs followed residents out of cities and suburban freeways made driving more time-competitive. Suburban riders often had enough political muscle to force money-losing operations to continue, and eventually Commuter Rail systems were given operating subsidies, allowing most to continue operation (although small systems in Pittsburgh, Cleveland and Detroit disappeared entirely—and Boston came close—and some lines in other cities were abandoned as well). What midday service existed was often cut back further, with some systems operating only at rush hour, and others with minimal midday service.

By the 1980s, subsidies and investment helped to improve some systems, and coupled with increasing congestion and parking costs, ridership began to improve. Before the pandemic, commuter railroads were often some of the least-subsidized forms of transit, recouping costs mostly by charging higher fares for their whiter, more-suburban ridership base while, in many cases, maintaining a 1950s operation on 1850s rights-of-way with 1950s rolling stock. This is the paradox of commuter rail service: by utilizing centuries of investment in the railroad, most of the costs are fixed. Original capital costs were paid generations ago, and many operating costs—maintenance of way, stations, signals—don’t vary depending on the amount of service provided. There is an almost-happy medium—which was attained in some cases pre-pandemic—where thousands of commuters drove to parking lots, boarded clunky, diesel trains (or, in some cases, newer electric trains on clunky, old tracks) for a ride to the city and back because while the experience may not have been particularly pleasant, it was preferable to bumper-to-bumper traffic.

Six cities have maintained this legacy service (Boston, New York, Philadelphia, Washington, D.C., Chicago and San Francisco). In the past 20 years, there has been some investment in new commuter rail systems, almost entirely on existing freight rail corridors (or parallel rights-of-way). In 2019, as measured by passenger-miles, 62% of commuter rail riders were in New York City, 12% in Chicago, and almost 90% in the six legacy cities (and 85% of fixed guideway passenger miles overall are in these cities). Los Angeles has built a system larger, by passenger-miles, than DC or San Francisco, but only by building a sprawling system with more track-miles operated than any other system but New Jersey Transit, which has rail lines in three states and includes operations into both New York and Philadelphia. (Metrolink carried about 400 million passenger miles in 2019, New Jersey Transit carried 2 billion. Commuter rail in New York had 8 billion rides: 20 times more than Los Angeles on a network only three times the size.)

Measuring passenger-miles is a measure of outputs, and is sort of just a stand-in for the system size and development patterns, plus factors such as the portion of the region served. Caltrain serves only one corridor in the region, but if San Francisco included BART—a system which derives significant ridership from its outer branches which act as commuter rail, albeit with much better frequencies—it would be the fifth-highest agency in the country by passenger-miles, trailing just the New York City’s subways and commuter rail agencies.

I wondered if I could measure inputs, as in, how much service is provided for each mile of track. Since so much of the cost of providing service is fixed (already paid for), the marginal cost to run more trains (which, in many cases, just means running existing rolling stock more frequently at off-peak times) is quite low. Luckily for me, the National Transit Database requires transit operators to report this (all data here is from the NTD’s 2019 data set; 2022 may begin to paint a reasonable post-pandemic picture but it won’t be released for months). I am also more interested in the number of trains operated as opposed to the number of cars operated; as a passenger, a two-car train every 15 minutes is far superior to an 8-car train every hour, and the NTD tracks this as “train miles.”

So I came up with my utilization intensity metric for fixed guideways: train miles per fixed guideway mile. It’s basically looking at frequency, but over an entire network. I then separated these by mode and agency and sorted them from lowest to highest. The results are not especially surprising, but do paint a bit of a picture of how American transit does, and doesn’t, work. (The data used here can be found in a Google Doc here.)

In the chart above, colors represent modes, where orange is heavy rail, blue light rail and gray commuter rail. Not surprisingly, New York City’s subway system is by far the most intensely-used system in the country. For every mile of track, there are more than 80,000 train miles per year, meaning that on average there is a train approximately every 6.5 minutes. PATH comes in second, followed by the MBTA’s Green Line, which ranks highly since its four branches are interlined in a high-capacity tunnel. The next ten slots are about evenly split between large heavy rail networks (Chicago, DC, Boston) and big-city light rail networks (San Francisco, Seattle, Houston, Minneapolis) which, in some cases, are being asked to perform a role similar to a heavy rail system, with grade separation, tunnels and long vehicles.

Most heavy rail networks cluster at or above 40,000, meaning a train, on average, every 12 minutes, inclusive of off-peak and overnight times. Many smaller light rail systems fall in the 20,000 to 35,000 range, which still means that they provide service every 15 minutes during much of the day, but in some cases with 20 or even 30 minute headways at off-peak times on less-used systems. And eventually, we arrive at our most intensely-used heavy rail system, two of which are above an inflection point where usage begins to drop. Given that two-thirds of commuter rail ridership is in New York City, it’s got to be in New York, right?



There’s a lot to fault about Denver’s transit system: that it follows freeways and doesn’t serve existing populations, that Colfax should have had a light rail line years ago, that new light rail and regional rail lines are sometimes built with huge parking lots instead of development, that it somehow took three years to figure out the crossing gates on the airport line, and that the light rail maybe should have been regional rail to begin with anyway.

But Denver did, and does, two things right. First, they built a 23 mile rail line in 2016 for $1.2 billion. Yes, the line follows existing rights-of-way (but separated from the freight railroad, because we can’t have nice things), but at an inflation-adjusted cost of $65 million per mile, which includes grade crossings, several flyovers, signals, full electrification, stations and rolling stock. Second, they run the service as frequent regional rail, not commute time-focused commuter rail. Which means that it is the most frequent commuter rail system in the country.

Denver’s airport service runs every 15 minutes from 4 a.m. to early evening, and then every half hour until after midnight on weekdays. And on Saturdays. And Sundays. Philadelphia has an airport service too. It’s run with the same electrified rail cars Denver uses, on a fully grade-separated line with double track the full route (Denver manages 15 minute headways with a portion of single track). It runs every 30 minutes on weekdays … and every hour on weekends (and this is still more frequent than most of Philadelphia’s “Regional Rail” lines). Denver and Philadelphia have the same level of past investment in their rail networks: electrification, grade separation, and in the case of the Airport Line in Philadelphia, level boarding. But Denver provides more than twice as much service.

The next two commuter rail agencies are in New York, MetroNorth (which nearly matches Denver) and the LIRR. Long Island and New Jersey fall down this list because they include more low-frequency tails which provide infrequent service along exurban and even quasi-rural routes (like the Port Jervis Line or Greenport, which only sees four trains per day). Then there’s SEPTA, which despite running trains only every two hours on weekends on some lines and hourly on weekdays still runs more service than other agencies. Beyond that, some newer systems, including in places like Texas, Florida and Utah, provide more service than the two largest non-New York systems: Metra in Chicago and the MBTA in Boston.

Metra doesn’t many good excuses for its lack of service. Before the pandemic, Metra services were very rush hour-focused. Take, for example, the heavily-trafficked BNSF line. With three tracks, Metra ran complex local/express service, filling trains at bus transfers and park-and-rides in the suburbs and depositing them in the city. 11 trains arrived in Chicago between 7 and 8 each morning, and another 12 between 8 and 9. The rest of the day had service every hour, and on Sundays, trains ran every two hours. More trains arrived in Chicago between 7 and 8 a.m. on a weekday than the entire day on Sunday (the 2019 summer schedule added a test train on Sunday morning and afternoon to provide hourly frequencies during part of the day).

One somewhat-reasonable excuse is that the BNSF Line, like some other Chicago-area lines (but not all), had heavy freight traffic, with dozens of freight trains operating each day. These trains were relegated to operating at non-peak times (at peak hour, passenger service occupied all three tracks), so the morning rush hour level of service wouldn’t be possible. Still, service every 30 minutes (or even 20 or 15) could be provided, potentially with some schedule padding built in for freight interference moving on and off of the corridor, with strategic investments to improve conditions (and, maybe some strategic reforms to the freight rail industry as a whole). With changing travel patterns post-pandemic, Metra is looking to move away from the high commuter skew (it has already cut schedules back at commute times based on demand) towards a more regional rail system.

Boston doesn’t have this excuse. While Chicago is the major freight logistics hub in the country, freight rail in and around Boston has dwindled to a few carloads per week aside from some through traffic that crosses the ends of a couple of the regions Commuter Rail lines. The MBTA controls nearly the entire network, and can not point to dozens of freight trains as a reason it can’t run more midday service, and it runs less service than Chicago. During the pandemic, the agency has moved to hourly service on most of its lines on weekdays (still every two hours on weekends) but in 2019 it ran 20% less service than Metra, and only 1/4 the service of Denver, despite similar base infrastructure (two-track railroad with minimal interfering traffic). This means that cities like Boston and Chicago are doing far less to leverage past investment than they could. Traffic congestion has returned—Boston is ranked fourth in the world—but with trains every hour or two, there’s little reason for most people to try to take one. The MBTA has given lip service to a “rail transformation” but actual policy has been at best lacking at at worst forays into technologic gadgetry.

The bottom of the list is populated by smaller systems: regional systems like the Keystone service between Harrisburg and Philadelphia (which, fun fact, is by far the fastest transit service in the country, averaging 56 mph) or the Downeaster from Boston to Maine (which is … not as fast). Aside from LA’s sprawling system, others are usually single-line systems in smaller cities, or, in the case of MARC in Maryland, a full-service line (the Penn Line) with rush-hour-only service on other line dragging down the average.

For other systems in cities that don’t rhyme with “Enver” there is a good policy outcome: running more trains. Everything needed to do this is in place: track, signals, trains, stations and probably even interested passengers. It requires little more than some additional staff and some additional fuel. With peak demand lower, it’s time for commuter rail agencies to be dragged, kicking and screaming, into the 21st century. Except for Denver, they’re already here.

Highway medians and calculating curves with Google Maps

(And, 2024 update, bonus on long, tall arch bridges!)

I haven’t posted here in a while (year and a half!) but with the demise of functional Twitter and figuring out HTTPS on my site (which … took me longer to do than it should have, sorry to everyone who attempted to enter their credit card to give me all the money and wound up giving it to a Nigerian Prince, but, really, I have a Patreon, it’s for my ski-related podcast but you can certainly click buttons over there) I figured it was time. In any case, I have a new job, I can probably not post about a lot of things, but now instead of long, ramblingTwitter threads, I’ll probably just post long, rambling posts here. Anyway …

Alon wrote a blog post nearly a decade ago about using highway medians for rail, and the differences between the US and Europe. It’s informative and mostly on-point, but I think he missed a couple of nuances and I’m going to go down a rabbit hole about a couple of them, specifically a) that roads are often less curvy than design limitations (with a nifty Google Maps way to measure that) and b) in most cases, European motorways/autobahns do not have wide medians, while North American roadways often do.

Highway medians: Europe vs America

First, a story: this summer, I was in Berlin (having gotten there from FRA via 9€ train), and was supposed to take a train to Frankfurt, meet my girlfriend (2024 edit: my wife!), and take another train (or maybe the same train) to Switzerland for some mountain time. Instead, I got the covid, got holed up for a few days, and walked around Berlin and looked at tram tracks. In a fit of genius, she suggested we rent a car and drive the die Autobahn mit the windows down (she’d been exposed along with me and had had it a few months before, so this seemed like a reasonable precaution) and so we rented a car at BER (which exists!) for the trip south to almost-Basel (much more expensive to return the car in CH than DE).

Was it how I had planned to cross Deutschland? Nein! But it was an interesting trip. My experience driving stick is limited to 20 years ago in New Zealand and a few days practice on her Fit. But once I got into gear in a rest stop, I could handle the autobahn fine (I even made it through a traffic jam, sorry, someone else’s clutch). I topped out at 183 km/h, slower than the ICE but plenty fast with the windows down. Sidebar to the sidebar: driving the autobahn is very civilized. There are rules: no passing on the right, overtake and then change lanes, no trucks on Sunday (this was a Sunday) and 100 mph didn’t feel that fast. 120 did, the Opel handled it fine, and I kind of wish I’d looked up the premium for renting a BMW. After 900 km we stumbled into a Michelin star restaurant (quite accidentally: it had the cheapest single rooms in Lörrach) and had a lovely meal that I could mostly taste.

Anyway, one thing I (sort of) noticed at 100 mph was that the autobahns do not have wide medians. There are some exceptions; like crossing the Swabian Jura between Stuttgart and Ulm, where the A8 splits into two roadways a mile apart, once of which runs on an old bridge under the Filstal high speed rail viaduct. with some gnarly curves, apparently this is a dangerous part of the network. But in general, medians for rural highways in Germany are only a couple of meters wide. France, too, where they sometimes get by with just a metal guardrail. Italy, Poland, Britain, Spain all seem the same.

Last year, the Wendlingen-Ulm high speed line opened along Autobahn 8, and outside of the aforementioned area (where it’s mostly tunneled) much of it follows along the side of the A8, because there’s no median. A side-running routing means that exit ramps become complex to build (such as here, in Merklingen), requiring much longer bridges and complex entry and exit ramps or, in this case, a tunnel. Putting the railroad in the median would obviate the need for any of these issues, especially retrofitting rail into an existing roadway layout, but those medians don’t exist in Europe.

They often do in the US. Newer roadways in open, rural areas often have medians which are 50 feet wide or wider. In many cases, these are grassy medians which do not require any guard rails, the assumption that if a car goes into the grass it will decelerate enough before it crosses to the other side. The medians can also be used for drainage when they slope down between the roadway.

As such, there are a number of Locations in the US where railroads already exist in highway medians. Several of these are transit lines in urban areas, where—to vehemently agree with Alon—they don’t belong (in many cases, the roadways were designed to accommodate rail lines, or even replace them). The width of these medians (between inside solid yellow lane lines) varies, and none has high speed rail:

LocationWidth (ft)TypeNotes
I-25 New Mexico100CRRetrofit, single track but designed for 2.
DC Metro65HROften in roadways designed for rail, several examples.
Chicago46-75HRWider Congress originally designed for 4 tracks
SF BART55HRDublin, other examples exist.
Albany, NY46FreightUrban area
Portland58-82LRWide inside shoulders
LA C Line /
Century Fwy
35-55LRBuilt 1980s-1990s, light rail included as mitigation.

Many, if not most, rural interstates have wide medians. To route a rail line alongside in very rural areas, it doesn’t matter much if a median is used or not: exits are widely spaced there’s plenty of room to rebuild them, and sticking to a median may require shifting over or under the roadway for curves, so it depends on the roadway curvature. Cities rarely have wide medians and they’re decidedly bad places for transit anyway. There are, however, “happy medium” areas where median-aligned rail might make sense, especially in more built-up areas where highways have wide medians and railroads could benefit from higher—if not truly high—speeds.

Measuring curvature with Google Maps

Alon’s other again-valid point is that sticking to a median means sticking to the curve of the roadway. Such an alignment may require constantly varying speeds, which is not exactly good for high speeds (see, for example, the Shore Line in Connecticut). But many roadways with wide medians are straight—or close to it—and would allow higher speeds. It’s hard to figure out curve radii using just Google Maps so I’ve created a bit of a cheat sheet. If we assume that highway lanes are 12 feet wide (in general, they are), we can draw a chord across a curve tangent to the second lane of the roadway using the measure distance tool (right click to activate it):

This example, in Newton, Mass. where the Turnpike is adjacent to the railroad, shows a 600 foot chord, which, if you do the trigonometry, traverses about 18˚ of a circle. US railroad curvature is measured as “degrees of curve per 100 feet”, which in this case is about 3˚. (I selected this example because I happen to know current speed limit here—55—and a resource with the curvature, although the original railroad may have been slightly straighter.) This corresponds to about a 575 meter radius. This can be extrapolated outwards as follows (approximately, see also this conversion table, and speed information here):

Chord (feet)DegreesRadius (m)Speed
4006.8260real slow
6003575~100 km/h / 60 mph
6502.6675~120 km/h / 75 mph
8001.71020~150 km/h / 90 mph
11000.911925200 km/h / 125 mph
13000.652690250 km/h / 150 mph
16000.434070300 km/h / 186 mph

Note that this can also be done in metric, and it can also be done by drawing chords on the inside of standard gauge railroad tracks. The calculator has information for both metric and imperial for both highway (two lanes) and rail tracks. (You can probably save a sheet as your own and change the values to pretty much anything else.)

Where median-aligned rail makes sense

Absent steep grades, roadways with sharp curves are not really suitable for true high speed rail. Even a road like I-95 in Connecticut has several 700-foot-chord curves which would limit speeds to about 80 mph in a few places, so the median might not be suitable. Still, a route along the Connecticut Turnpike would probably be much faster than the Shore Line: some of the sharpest curves have a wide median which could allow smoother curves, tilting trains could improve speeds, and the curves on the Shore Line are far more restricting. Several other Interstate highways in the northeast have similarly restrictive curves. And older and more urban highways often have narrow medians anyway.

That said, there may be other opportunities to leverage our wide medians in the US. Back when I blogged more regularly, I proposed routing South Coast Rail via a stretch of 495, which has a 100-foot-wide median. (This somehow pissed off people in Taunton, who didn’t want a good idea to get in the way of the current iteration of SCR.) The only appreciable curve this encounters on 495 is a 1200′ chord, so … fast (getting to 495 would be trickier). Whenever I drive up I-95 to New Hampshire I think about how straight and wide the highway is and, yes, it could support high speeds (but it doesn’t really connect anything). Out in California, I-5 on the west side of the Central Valley bypasses every population center between LA and San Francisco, but if California HSR had used its median instead of the debacle of going through the Central Valley cities, it may have allowed a much easier path to construction in the valley.

Sometimes “high speed rail” is thrown about by people with no idea what they are talking about. Like as a solution to I-70 traffic in Colorado. Certainly not in the too-narrow median, but also not along the highway with sharp curves. (In Europe they’d just dig a base tunnel, of course, the mountains in Europe are narrower.) And then you have the Connecticut NIMBYs saying to build an inland route along I-84 which … has hills, curves and development. The same ones who killed I-95 high speed rail because highways adjacent to historic sites are fine, but highways and trains next to historic sites are bad. (To be fair, the Lyme portion of I-95 has a narrow median, and 900m curve radii.)

Virginia S Line

Too often, railway planners don’t even consider the potential to use a highway median. The S Line project between Raleigh and Richmond is illustrative of this. It will use an existing railroad right-of-way, with many curves mitigated for higher speed operation, and new grade separations to create a fully grade-separated railroad (albeit not too many as it runs through a rural area). Most of the railway, especially in Virginia, runs parallel to I-85, which has a wide median (mostly 180 feet, a few sections near exits are closer to 80 but those have pre-built grade separation). Rather than re-engineering the parallel, abandoned rail line, a high-speed line could be laid in the highway median (the sharpest curve is about 0.5˚/3000m radius, which might limit speed at three short segments to about 165 mph, but given the width of the median the railroad could traverse a wider curve and maintain higher speeds.

The median here is mostly in a “natural” state, or about as natural as a treed-in area between two road carriageways can be. This would require considerable disruption of this “habitat” since it would leave only a small strip on either side (or, the trees would be removed entirely) which may have additional environmental burden compared to an existing, if long-abandoned, rail right-of-way. But since the parallel rail right-of-way will require several miles where the railroad will be rebuilt to be straighter, the highway median might be a more prudent choice, minimizing new grade separations and maximizing potential alignment for high speed.

Notably, this wouldn’t work as well in North Carolina. For whatever reason, while Virginia’s highway engineers left a wide median, North Carolina’s did not. The median narrows at the border to about 30 feet (portions of the road do have wider medians, but nothing like Virginia). It’s also more populated; the section between Henderson and Petersburg is only shown with one station in 920-person Norlina; the I-85 alignment would bring it closer to South Hill which, at nearly 5000 people, is the largest town in this 90-mile stretch by a wide margin (thus using the highway median won’t give up ridership). Meanwhile south of Henderson, the rail line goes through the fast-growing suburbs of Raleigh of Wake Forest which, notably, is not home to Wake Forest University (it moved 100 miles west to Winston-Salem in 1956). Following the highway alignment past Henderson would be more complicated and aim away from Raleigh and instead at Durham (serving both will require some amount of deviation, and there’s no reasonable right-of-way to Chapel Hill, but Richmond-Raleigh-Durham makes more sense since it then aims towards Charlotte and Atlanta; if there were ever demand a bypass of Raleigh could save about 25 miles). Further south in North Carolina, I-85’s median is often narrow, the roadway itself has more curves, and at one point crosses over itself for a mid-highway rest area. North Carolina’s highway engineers are cut from a different cloth.


Sometimes, planners use medians too well. Two high-speed rail projects which are in operation or planning are Brightline in Florida and Brightline West in California. Neither is without issues: Florida’s only has a few miles of high-speed operation (and it’s not so fast) but was built inexpensively along a very rural (and being Florida, straight and flat) highway. Where it does cross exit ramps, it required significant ramp redesigns or slower rail speeds (crossing Route 417 requires a 90 mph curve). Brightline in Florida has shown latent demand for mid-speed rail projects (although the Borealis train in the Upper Midwest has shown high demand using existing infrastructure).

Meanwhile, out west, Brightline’s next project is to connect Vegas and LA. And by Vegas I mean “near the strip, kind of” and by LA I mean “somewhere east of LA.” Downsides: lots of single track, the median isn’t as fast as it could be (curves, and some narrow sections). It won’t be faster than flying for most trips, and will only beat out driving at high-traffic times (which to be fair, because LA, is a lot of the time), and it will be hard to scale by speed or capacity, but it will be high speed rail, even if, going from exurbs to far-from-the-city-center and mostly single-tracked, it would be laughed out of Europe. (There are a number of European lines with stations far from city centers, but those are mostly smaller cities and towns mid-route, not major end-of-route destinations.)

There’s also the question of “can you build a new 220-mile right-of-way in four years?” Yes, the Florida version only took four years to build (if you discount some early work moving some exit ramps). But it was a simpler project: about 20% of the distance, no electrification, and much closer to an available workforce, with only one significant roadway reconfiguration (the Beachline east of I-95). If they can get this built, good, although hopefully it doesn’t encourage an American version of high speed rail with single tracking to save money but which inhibits future capacity.

A local proposal: Cape Cod?

My interest was recently piqued by the continuing failure of the Cape Bridges project to garner necessary federal funding. Maybe the Feds are just not that interested in giving a couple of billion dollars to some bridges which are only at capacity a few days per year, and which MassDOT wants to widen (although they are nearly a century old). Of course, there is no mention of improving the rail link to the Cape, which currently takes 2:20 to get to Hyannis, an hour longer than driving without traffic (rare!).

In a civilized country, the Cape would be a transit-first destination. It has 220,000 year-round residents, 500,000 summer residents and significant additional short-term tourist traffic, and its 339 square miles include 100 square miles of National Seashore and military reserve. The two bridges crossing the canal create bottlenecks; when they were build in the 1930s, Barnstable County only had 32,000 residents. The Cape is a narrow peninsula which could be well-served by an arterial transit line, has many destinations with limited parking, and is most heavily-used in the summer, when bicycles should be a major transportation mode. Trips to the Cape include access to island ferry terminals: the islands have year-round populations of about 30,000, but nearly 10 times that in the summer, with the Steamship Authority providing half a million trips per month during peak season, plus other private ferries, with thousands of cars parked at mainland ferry terminals and minimal transit connections.

In America, transit on the Cape is barely an afterthought. Good transit would require a combination of useful local transit, safe bicycle facilities and various ways of discouraging traffic, a fast train to Boston, Providence and beyond, and special notice given to transporting people to the island ferry terminals since many of them have to park far away and board a shuttle already (so why not shift the shuttle of the other side of the bridge?). Density would help but wouldn’t be easy: one reason development on the Cape is so spread out: It was developed without a sewer system. (Building one ain’t cheap, and those chickens are coming home to roost.) As it is, there are commuter buses subjected to the same traffic as cars, a regional transit authority providing hourly service at best (although their route between Orleans and Provincetown does have the latest scheduled departure in the state, a 1:30 a.m. trip, and serves many workers priced out of the Lower Cape), and three train trips per week in the summer, which run on an existing commuter line, a straight line on the mainland at reasonable speeds before crossing the old lift bridge, and then at speeds charitably described as “pokey” on the Cape itself. CapeFlyer, which I wrote about in 2015, is a nice alternative for some but is not making much of a dent in traffic.

Imagine a high speed link from Middleborough to Hyannis. The line would transition to the median of 495 (sharpest curve: ~1500m) and where 495/Route 25 curves towards the Bourne Bridge, follow a power line right-of-way cross the Cape on a new fixed crossing where the canal splits two hills and is already crossed by power lines, eliminating any need for long ramps to attain grade. (More about this bridge below.) From there, the power lines lead to the Midcape Highway, which has a narrow median at first (but borders miles of state-owned military reserve) and eventually has a wider one. For most of the Midcape, the State owns a 400-foot-wide cross-section, and much of it includes a 100-foot dividing area between a service road and the highway itself. The worst curves there are also about 1500m, there are no long grades (although a couple of instances with grades above 3% which might need some earth moved), and the underlying topography is a glacial moraine so no need for significant blasting. So while the highest speeds might be off the table using a median alignment, averaging 100 mph—which would allow a trip from Middleborough to Hyannis in about 24 minutes and a trip from Boston in just over an hour—would be attainable.

I’m sure people would yowl about ruining the pastoral feel of the partially tree-lined highway median. And a train below a power line would harm the environment to no end. As for what to do with the existing railroad? With transit (and the trash train) moved to a new, faster corridor, it would be a great extension of the existing rail trail, since the portion east of Hyannis is relatively sparsely-populated and could be served by parallel highway-aligned stations. This would allow the popular rail trail to run from the canal to Wellfleet (beyond which the right-of-way is no longer intact, although the state is planning safer bicycle facilities along Route 6 to Provincetown).

Highway medians are certainly not always the answer for rail lines: they have to be wide, straight and flat enough and serve a desired path of travel. They also are suboptimal in urban environments, where the highway can be a barrier to potential rider access. Elsewhere in New England, there are few good examples:

  • The Turnpike west of Boston is neither wide, straight or flat, and improving the parallel existing railroad is a better alternative.
  • I-95 to Providence has a wide median but is paralleled by one of the few high speed rail segments in the country.
  • In Connecticut, the highway might be useful to bypass the curvy shore line in the eastern part of the state, but is shoehorned in amongst sprawling suburbs further west, where improvements to the existing New Haven line are probably a better investment.
  • I-91, I-84: hilly, curvy, narrow, or all of the above.
  • I-95 north of Boston is straight, wide and flat and would make a good segment of a higher-speed line to New Hampshire and Maine … if only it connected anywhere near the existing railroads.
  • Elsewhere in Northern New England: curves and mountains, although the 15-year, nearly-a-billion-dollar reconstruction of I-93 in New Hampshire may have left room so as not to preclude an eventual rail line.

Given enough width and straight enough corridors and a good route profile, they can provide a good alignment for some new medium- to high-speed corridors. This requires both wide-enough medians (rare in Europe and hardly a given in the US) and straight- and flat-enough alignments. When these ingredients come together, highway medians can provide a potential lower-cost, politically expedient means of building a railroad.

Oh, about that Canal bridge … 

It’s worth remembering that Cape Cod is a terminal moraine and related glacial outwash which was formed at the end of the glacial ice sheets which covered New England in the not-too-distant past. (So are Long Island, Nantucket and Martha’s Vineyard, here is a useful publication.) Notably, as shown on the map below, two moraines from glacial ice lobes meet near the canal, creating a narrow cut with steep hillsides on either side (magenta).

The magenta here shows the terminal moraines which meet near the canal, which cuts through them. This creates the hill through which the canal was cut. From the USGS.
The moraines are easy to see on this digital elevation model (original link broken, but from this general vicinity), intersecting near the canal. I guess I wonder why the canal didn’t go slightly further north where the hills are lower.

Between the tops of the hills at this point the canal and its cut is about 2100 feet wide (in this image the power line supports sit on top of the nearby hills). The canal itself is 700 feet wide, although the navigable portion is just 480 feet; the Bourne and Sagamore bridges’ longest spans are 616 feet with supports in the edge of the canal. 600 feet is not a particularly remarkable length for a bridge: the Hell Gate Bridge has a span of nearly 1000 feet (and miles-long approach spans, something which wouldn’t be necessary here).

In Germany, the recently-completed Erfurt-Nuremburg high speed line has several bridges of interest, the longest of which are the Grümpentalbrucke (Germany finally has some streetview) and the Talbrucke Froschgrundsee, each a 270 meter span. The Talbrucke Froschgrundsee is 65m in height (it’s unclear if this is to the top of the bridge or clearance below; in either case, much higher than the Cape Cod Canal clearance of 41m) and cost 16 million Euros to build in 2008 (adjusting for inflation and currency, about $36 million today).

Even more impressively, the Almonte and Tajo bridges near Cáceres in Spain are both more than 300 meters long and 70 meters high. These bridge were built over a reservoir with strict environmental guidelines which didn’t allow any construction in the water itself. Also, these concrete arch bridges are visually interesting, and would be a dramatic addition to the landscape and possibly a net positive (especially if the power supply were put into a conduit on the bridge and the power line towers removed).

Closer to home and present, the new bridge over the Genessee River in Letchworth State Park in New York was completed in 2017 for $71 million (for a single track). The current lift bridge to the Cape is just as old as the fixed highway bridges, and replacing it with a fixed, higher speed crossing could pay long-term dividends.

Why not a tunnel? A tunnel wouldn’t take advantage of the topography, and because it would have to clear well under the canal, it would require a long approaches on either side. On the mainland side, it would need to go from about 100 feet above ground level to 100 feet below, and on the Cape side from 200 feet above to 200 feet below. Even with a 3% grade, this would require about a mile and a half on the mainland side and two and a half miles on the Cape side, plus half a mile under the canal, meaning a five mile tunnel versus a half mile bridge.

MBTA Commuter Rail Fares Used to Make Sense*

[* Kind of, and only at certain times of day. They don’t anymore.]

Before the pandemic, the MBTA relied on Commuter Rail fare revenue. In 2019, the service accounted for less than 9% of total transit system rides (about 32 million) but 36% of fare revenue: about $250 million dollars. While bus and transit fares are relatively low, flat fares ($1.70 and $2.40, with free transfers), Commuter Rail fares start at $6.50 (with a few exceptions) and go up from there, to more than $12 for trips extending more than 30 miles from Downtown.

There are exceptions. Fares within 6 miles of Downtown Boston, including to Chelsea, West Medford and Allston, are priced the same as a subway ride. The Fairmount Line, which serves low-income neighborhoods of Boston, is priced at the same, lower level. “Interzone” fares, for trips between outlying stations on the same line, give about a 50% discount compared to a trip from the same station to Downtown. Overall, fares per mile are about the same as for trips on the bus and rapid transit system (35 to 40 cents per mile), although Commuter Rail fares per mile vary considerably: a trip from Belmont to Boston costs $6.50 for 6.5 miles ($1 per mile) while a trip from Worcester costs $12.25 for 44 miles (28¢ per mile).

There was some sense to Commuter Rail fares. The Commuter Rail system was optimized for a balance of fleet constraints, overall public utility and fare revenue, and generally in that order. But only at rush hour.

Transit systems have very high up-front costs to provide a base level of service, but the marginal cost of adding passengers to this base level of service is nearly zero. In the case of Commuter Rail, the fixed costs involve the right-of-way (capital costs and maintenance), maintenance facilities, signaling, control center, customer service, stations, and other fixed assets. These costs are fixed, whether you run 1 train per day or 100, and account for much of the cost of the railroad. The first decision the agency has to make is the base level of service: how many trains to you need to provide an even level of service during the day.

Pre-pandemic, the Commuter-oriented system set this at a very low level. In general, trains ran about every two hours on each line (you can find an archive of schedules here). In some cases, trains were slightly more frequent (the Lowell Line had hourly weekday service), but two hours was normal on most lines, even those to Providence and Worcester. In addition, since most trains spend the night at outlying terminals, they need to be serviced and fueled at downtown termini, meaning that trains would be cycled in and out of these every-two-hour service levels for service (although fueling and inspections do not necessarily occur daily). So the baseline cost of running the service depends on the number of trains needed to run the service at this interval, plus to cycle trains to and from centralized maintenance facilities.

In the case of the MBTA’s Commuter Rail system, the agency needed approximately 25 trains to provide this base level of service, so about 35 including trains being serviced (the rest are stored Downtown or elsewhere), of the 65 train sets operated each day.

The next decision, which is based on the base level of service, is how much additional service to add at rush hour. The cost of adding some service at rush hour is relatively low: the trains which are being serviced during the base period can be pressed into service, so the marginal additional costs to rush hour service comes mostly from additional labor. Beyond these trains (about a 50% increase in service, so a train every 1:20 or so), however, costs for additional service increase quickly. To operate a rush hour-only train the costs include:

  • The cost of additional labor, which often results in a split shift where the staff works in the morning and evening with a “midday release” during which they are paid half-time.
  • The cost of midday layover facilities, or “parking spaces for trains.”
  • The cost to operate empty trains to and from these midday layover locations, which in some cases are up to 10 miles from the terminal station. In the case of the T, this meant finding room for about 30 trains during the middle of the day. (I’ve argued before that these trains would be better used providing more service).
  • The costs for the actual additional trains. Before the pandemic, three Commuter Rail train sets made just one round trip per day, and several others made just two, meaning that they were idle for 19 to 21 hours per day, so the capital cost of a train set (about $25 million) had to be amortized across this limited service. (The single-trip trains were generally the longest, largest trains, with 8 or 9 double-decker coaches carrying nearly 2000 passengers.)

The MBTA generally scheduled as many trains as they could fit on their lines without major capital improvements. There are several limiting factors to the number of trains, including often-antiquated signal systems, sections of single-track, and terminal design and congestion. The number of trains varied by demand by line (which, in many cases, depends on parking lot capacity, since the T has made the (poor, in my opinion) decision over the years to create park-and-ride stations and not stations with high density housing nearby), line capacity, and congestion at each terminal. In some cases this meant four trains per hour, in some cases fewer than two.

Given this service, there are two ways to set fares. One is to maximize the utility of the system (getting as many people onto each train as possible) and one is to maximize revenue (set fares where they will generate the most revenue, even if it means fewer passengers). The T’s fares sort of split the difference. The fares are almost certainly not revenue-maximizing; every fare increase analysis has shown that when fares are raised, ridership drops, but the elasticity is such that it drops by less than the fare is increased. Fare maximization would have less-frequent trains (reducing marginal operating costs) carrying only the riders who for whom the train was time- and cost-competitive with driving. In fact, such a system might have come close to revenue neutrality. Running emptier trains, however, would mean more people driving on the road and more congestion and pollution, which have regional negative externalities.

In general, the agency matched passenger demand to train size, meting out train cars across the system based so that the trains would be full, but not too full (when smaller sets had to be substituted in, passengers were sometimes left behind). If fares were much lower, the trains in the system would not have been able to handle the crowding. So if the MBTA’s Commuter Rail fare system was optimized in any way, it optimized overall utility given the fleet and system constraints, and then revenue maximization given the utility. There’s nothing inherently wrong with this.

Now, is this actually how Commuter Rail fares were set? Of course not, that would make too much sense. Commuter Rail fares are higher because Commuter Rail fares have always been higher. Before the Commuter Rail system was integrated into the MBTA, fares were even higher than today. In 1971, a fare from Malden to Boston (before the Orange Line was extended there) was 95¢, versus a 25¢ subway ride. The equivalent of a Zone 1 fare was $1.10 and the equivalent of a Zone 8 fare was $2.20, which would be $8 to $16 today (these distance-based fares—in 5¢ increments—were changed to zone fares at some point during the 1970s, and multi-ride tickets were offered with a 20% discount, similar to passes today but without any reciprocity on subways and buses). Since the system was, at the time, operated by private carriers with an agency subsidy, they were more interested in maximizing revenue than utility (they certainly weren’t interested in providing service, and provided very little).

Once integrated into the MBTA, fares have generally been about 2.5 times that of a base subway fare for Zone 1 travel, with Zone 8 costing 4 to 5 times a base subway fare. Fares fell, relative to inflation, during the 1980s and 1990s (when Commuter Rail ridership grew most quickly), and have doubled, relative to inflation, since 2000. In 1999, the $2.00 Zone 1 Commuter Rail fare is equivalent to $3.31 in 2021 dollars, about half of the cost of a Zone 1 ticket today. While this increase is tied to rapid transit fares, and while commuters were willing to pay higher fares at rush hour, it has made the Commuter Rail much less price-competitive with driving at off-peak hours.

YearZone 1Zone 8Z1 2021 $Subway

Data from 1970 and 1971 taken from a photograph of a fare tariff posted at the Wayland Station in 1971, during the last months of service there.

There are two problems with this system. One, the optimization was only valid for peak rush hour! During the midday period, even with minimal service with trains every two hours, the higher fares were less competitive with driving. At rush hour, the trains could generally come close to matching driving times (in some cases bettering them) given congestion, and were less expensive than parking. (In theory, the pre-pandemic revenue-maximizing fare may have been closer to Downtown Boston parking costs.) At other times, service was slower than free-flowing traffic and more expensive than off-peak parking rates. Yet even though there was plenty of room on the trains, prices remained the same.

In 2018, the T introduced $10 weekend passes, a steep discount over normal one-way fares. These proved wildly successful, and the elasticity was such that revenue actually increased, providing much more public utility while netting the agency more revenue. (A flawed MBTA analysis attempted to cut the program short and did for a few weeks—they wouldn’t want to threaten the public with a good time—until the FTA told them that, no, it was fine, and to carry it forward.) Theoretically, a similar product could be used for midday service (for instance, unlimited daily trips for $10, excluding inbound trains before 9:30, similar to Metra’s Lollapalooza pass of years past). This was never proposed or instituted, because of the second problem: the pandemic.

Transit ridership cratered after the pandemic, but it fell unevenly. Bus ridership on some routes fell less than 50%, and in some cases has nearly recovered to pre-pandemic levels. Rapid transit ridership fell more, but is also recovering. But Commuter Rail ridership fell by more than 90%, and it is clear that the 9-to-5 Commuter Rail market is unlikely to fully recover any time soon. The MBTA has responded to the changing trip patterns on Commuter Rail by flattening service: in most cases, there are now hourly trains on all lines, no matter the time of day (weekend service is still less), with only a few cases with more frequent rush hour trains. This provides quite a silver lining for the agency: they can provide more base service, without having the costs of midday staff releases, midday train storage and trains which are only in use for one round-trip per day. Anecdotally, ridership during rush hours remains quite depressed, but midday ridership and weekend ridership has shown significant recovery.

Fares, however, have not changed with the service levels, since the fares are still optimized for the previous 9-to-5 commuting crowd. Traffic congestion has returned, and while the peak traffic is not as congested as before the pandemic, overall volumes during the day are as high or, in some cases, higher. With ample capacity on the improved-frequency Commuter Rail system, it could provide a significant utility to the traveling public if it was priced more competitively. Yet it retains its peak-hour pricing.

The MBTA could experiment with Commuter Rail fares to provide more equitable service and attempt a different sort of optimization, choosing to optimize public utility first, and not maximize fare revenue until and unless trains experienced crowding. It turns out, however, that optimizing utility might actually increase revenues, as was experienced from weekend fares. It could also be an opportunity to make fares less complicated with fewer zones and more day-pass options. Imagine the following fare structure:

  • $2.50 single trip in the MBTA bus/subway service area (basically inside 128, current zones 1 and 2), also available with a daily/weekly/monthly “link” pass.
  • $5.00 single trip / $10.00 daily pass for trips originating at stations between 128 and 495 (current zones 3 to 6)
  • $7.50 / $15.00 daily pass outside of 495
  • $2.50 for “interzone” trips (trips not originating in what is today Zone 1A)
  • Day passes also cover all buses and subways, single trip tickets allow free transfers to buses and subways.

This would set fares near buses and subways to the same price as the parallel transit service. In the past, the T has rationalized the higher prices on Commuter Rail by saying that if Commuter Rail prices were the same as local buses, too many people would crowd onto the trains (which may have been true). This is no longer the case! This fare system would mean that stations in places like Roslindale, Lynn, Waltham, Newton and Salem would have the same fare to Boston whether a rider took a bus, subway or train. That’s the product; moving people where they need to be. There’s no longer a capacity crunch excuse to price discrimiate. Furthermore, it makes the fare system much easier to understand. Instead of more than a dozen fares the T has today, it divides the system into three fare zones, and provides transfers between modes.

Beyond 128, prices would not be much different than prices in the late 1990s, when Commuter Rail ridership increased dramatically. With more midday service in these areas, there might be significantly more ridership at those times of day, since prices would generally be lower than driving and parking. And since the trains being operated have plenty of space, revenue may actually improve. It likely won’t hit the levels it did before the pandemic for some time, but we should be trying to maximize utility, not revenue.

The densest Census tract is not in New York

Or: why it matters where you draw boundaries. (Or, more specifically, the modifiable aerial unit problem. Thanks, Twitter.)

If you go to the wonderful and find the census tract with, in 2016, as close to 100,000 people per square mile as you can, you’ll wind up in Los Angeles (believe it or not). If you then click the “up” arrow, you can cycle through denser and denser census tracts, and you’ll see a lot of New York City (sometimes the map in the UI doesn’t even reload, but just recenters to a nearby tract). There are a couple of tracts in San Francisco in the 100,000 to 200,000 range, and eventually you’ll get to Le Frak City (click the link to save the trouble of clicking through) which, at 250,000 people per square mile, is the densest tract in New York (about 14,000 people living in about 1/20th of a square mile, give or take).

But go ahead and click the arrow once again.

The page will reload and you’ll be transported not to Brooklyn or Manhattan or the Bronx, but to Chicago. The tract in question has about 1600 people living in 0.003 square miles: two residential towers in Edgewater, on Lake Shore Drive, several miles from the Loop. It’s a bizarrely-drawn tract almost entirely surrounded by a much larger tract, and if the two were combined the resulting tract would be home to about 35,000 people per square mile, on par for the surrounding neighborhood but nowhere near as dense as much of New York City. (The second-densest current tract in Chicago is also made up of North Side high rises at about 90,000 per square mile, but the Robert Taylor Homes, which once housed 27,000 people on 95 acres, was in the neighborhood of 180,000. Cabrini-Green may have been denser still.)

In fact, New York isn’t even the densest city in the country, with several small cities across the river in New Jersey (and one Hasidic village in Rockland County) higher. Manhattan (New York County) is the most densely-populated county in the country at 70,000 people per square mile (although at its peak population in the early 1900s, it was over 100,000; on par with Manila). Two, three and four? Kings (Brooklyn), Bronx and Queens. Of course, New York State is the 8th most densely populated state, and that’s not counting DC, Puerto Rico, Guam, the Virgin Islands and American Samoa. It all depends on where you draw the line.

Which brings us to a New York Times article about downtown areas and their post-covid resilience. They use downtown areas, as defined by CoStar here (the website is a time capsule from the mid-2000s). The issue: there is huge variation between the size of the defined “downtown” areas: in some cases they carefully clip out non-housing areas, in others, they just draw a box around the downtown. The thesis of the article is:

What remain[s] at the heart of many cities in the 20th century [are] blocks and blocks of office buildings filled perhaps 10 hours a day, five days a week — a precarious urban monoculture. […] That means there are few residents to support restaurants at night or to keep lunch counters open if office workers stay away, and few reasons for visitors to spend time or money there on the weekend.

Here is how the story shows the downtowns for Austin and Boston, with the black bar showing a quarter mile. They appear to be similar in size, however, Boston is about 0.37 square miles, while Austin is 1.7 square miles. Not only is that a nearly 5-fold difference, but the Boston metro area is more than twice the size of Austin, so we’d expect a more agglomerated Downtown area with more office space.

The real kicker is that Boston’s Downtown, as defined by CoStar, is surrounded by residential neighborhoods, none more than a 10 minute walk away. Except for the area in the direction of Back Bay, the gray areas surrounding Downtown Boston include Beacon Hill, the West End, the North End, Chinatown and Bay Village, all residential areas. If you take the neighborhoods on the Shawmut peninsula and Beacon Hill, it adds up to about to about 1.5 square miles, with about 41,000 people. Slightly-larger Downtown Austin? It’s grown significantly in recent years, but still is home to only about 12,000 people.

Using the insizeor app from the BPL, here is the defined CBD of Austin overlaid on Downtown Boston. Note that it covers not only the Financial District, but nearly the entire Shawmut Peninsula, as well as parts of Back Bay and the Seaport.

In the article the CBD sizes range from Boston at 0.37 miles to New York, where the CBD is defined as “everything south of 59th Street” which encompasses 9 square miles (New York’s MSA is 5 times the size of Boston’s, but the “downtown” is 24 times larger). Minneapolis is 4 square miles, Saint Paul 0.67. In many cases, the “downtown” area is defined by the highways around it. Other cities, like San Francisco, have several defined districts defined as the “CBD”; San Francisco’s “Financial District” would probably rate similarly to Boston’s in the proportion of office space, and certainly as less office-dense than their Grand Central-defined parcel in New York.

So it’s true that in the Financial District of Boston itself there aren’t many residents. Yet a similarly-drawn box carved into Austin, or most any other city noted in the article, would find the same thing. Taken to a logical extreme, a small box around a single office building would be 100% office use. Or a single tract: there’s one in Midtown Manhattan with a population density less than 1000. There are just 44 residents in the tract bounded by 5th and Park avenues, and 42nd and 49th streets. Of course, just to the east, Murray Hill and Midtown East have 100,000 people per square mile. It turns out that aggregations of this size and variability are not appropriate for this sort of analysis.

Commuting and office use patterns will certainly change post-pandemic. 9-to-5 office districts may be less valuable, and some real estate may be converted to other uses: the article notes an evolution away from single-purpose downtowns. There may be a better metric of office density, perhaps using a certain land area based on the size of the city. But comparing wildly differently-sized “downtown” areas is like saying that, because the densest census tract in the country is in Chicago, Chicago must be the most densely-populated city in the country.