The curves of the River Route

Sharp curves along the Mississippi River rail route used by Amtrak's Empire Builder and Borealis. Red, orange, and yellow denote zones where curves dictate speeds of about 75 mph or less. Most of the route is currently constrained to 65 mph for passenger trains instead of the usual 79 mph limit.

I've recently been trying to wrap my head around the speed zones for passenger trains between St. Paul and La Crosse along the Mississippi River. A post from Korh on the UrbanMSP forums got me interested in taking a closer look at track curvature and the concepts of superelevation (banking or cant) and cant deficiency (underbalance, the amount a vehicle wants to swing outward).

I dug up Alon Levy's post about calculating speeds, and ended up using Ari Ofsevit's method linked at the end, which involves tracing lines from the outer rail to the inner rail and back out again to create chords to estimate the degree of curvature.

Example of drawing a chord between outer and inner tracks as a way of deriving approximate curvature, from Ari Ofsevit's spreadsheet

While observing Borealis trips on the asm.transitdocs.com tracker, such as this run on June 12th, I'd noticed that much of the route appeared to be limited to 65 mph, with only limited sections allowing 75 or 79 mph.

I was reminded today that the Midwest Regional Rail Initiative (MWRRI) had produced a report for 110-mph train service in the corridor, which included travel time modeling graphs. The graphs also show the attainable speeds for standard Amtrak trains in light green, confirming the mostly-65 mph speed zones:

Passenger train speed plot from Tomah, Wisconsin to north of Red Wing, MN showing a hypothetical 110-mph train in dark green (limited to 90 mph along most of the river corridor) and what a current Amtrak train speed would be in light green. (One of three graphs, travel time is likely for Milwaukee through St. Paul to Minneapolis)

 

At the speeds we're concerned about here, increasing superelevation by one inch or allowing one extra inch of cant deficiency in the rail cars translates to a speed limit increase of about 5 mph. For example, going from a combination of 3 inches of superelevation and 3 inches of cant deficiency to 4 inches of superelevation and 5 inches of cant deficiency would likely allow a 65-mph zone to become a 79-mph zone.

Selected probable speed limits given a combination of superelevation and cant deficiency in inches, color-coded to match the map at the top of this article. Increasing by the equivalent of 3 inches increases possible speeds by 10 to 20 mph in most cases. See the full calculator.

These appear to be the main factors that the MWRRI study used to justify higher speeds along the Mississippi River route—they planned to increase the height of the outside rail to 4" of banking whenever possible (the starting point is unclear, though they do mention 2.5" as an "optimal" amount on page 3-5 of the main study document), and hoped to gain another 2" from enhanced cant deficiency of tilting trains, going from a standard of 4" to 6".

Partial description of the guidelines used when modeling train speed and trip time, from the beginning on page 4-1 of the main MWRRI study document

Even with that, they only planned to have 90-mph speeds along the river, with a lot of curves requiring drops down to about 85 mph (although they neglected a few spots where 110-mph running appears reasonable: around Kellogg, around Frontenac, and between Red Wing and Hastings).

Alon Levy argues against tilting trains these days, saying they don't really provide enough speed benefit to justify their extra maintenance cost. They also note that other countries are running non-tilting trains with 180 mm (about 7") of cant deficiency, which is the same as what Amtrak has been allowed on their tilting Talgos and Acelas. (One of the limiting factor there may have been the heavy non-tilting locomotives rather than the passenger compartments, which are capable of much greater tilt and underbalance.)

As Alon notes, cant deficiency is primarily an issue of how the suspension system of a train behaves, so equipment with higher centers of gravity and softer springs/dampers will tend to swing further outward on curves than other train cars. Alon referred to a "magic HSR waiver" proposal, which might be in this federal register notice, where Amtrak proposed allowing higher cant deficiency on their trains following testing. In that notice, it suggested operators could apply to allow 4" on Superliner equipment like on the Empire Builder and 6" on single-level equipment like what the Borealis runs.

This Federal Railroad Administration freight+passenger superelevation study from 2019 didn't include rail height standards from Canadian Pacific, but did note that they limit cant deficiency to 3". Considering current speed limits on the river route, they presumably limit most curves to 2 to 3" of superelevation.

I believe the only Amtrak trains that have been using significant amounts of Canadian Pacific track until this year have been the Adirondack in New York, the Hiawatha between Milwaukee and Chicago, and the Empire Builder on our familiar route. It's quite likely that they've set standards based on the Builder's Superliners, so it would be worth having MnDOT, WisDOT, and even NYSDOT (since the Adirondack uses single-level trains) get together with CPKC and the FRA to determine if 1" to 2" of additional cant deficiency can be allowed with existing equipment, boosting speeds by 5-10 mph on curvy sections.

I haven't been able to find any allowable cant deficiency information for Siemens Venture / Amtrak Airo passenger equipment that is being planned/procured for many lines across the country.

There are some true limits when it comes to cant deficiency—you don't want a rail car to swing outward from an inner track to hit a slow or stopped freight train leaning inward, for instance. However, that's not an issue on single-tracked parts of the route, so those sections would be the best ones to increase speeds on to begin with. Most of the single-track sections along the river are 6 to 10 miles in length, allowing several miles of faster running at a time before needing to worry about adjacent freight cars.

If half of the speed gains on this section were just supposed to come from better equipment rather than major investment in the track itself, we should make sure we're using our existing and planned train cars as effectively as possible. It doesn't remove the need to maintain track well enough to remove bumps and wobbles on the smaller scale, but it would substantially lessen the need to increase banking on curves.