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.