Covering rail projects along the Twin Cities – Milwaukee – Chicago Corridor, and delving into the history of the Hiawathas, Zephyrs, and 400s which raced through this region in excess of 100 mph in the 1930s, '40s, and '50s.
Friday, March 29, 2013
Duluth train finishes major stage of environmental review
The proposed Northern Lights Express train from Minneapolis to Duluth ("NLX") took another step forward on Monday last week when the long-awaited Tier 1 Service Level Environmental Assessment was finally released. Initially expected to be completed by October 2011, the environmental review was delayed as the scale of the project was reassessed after early cost projections came in higher than expected. Since 2007, the route has been planned to operate at a top speed of 110 miles per hour, though the proposed length of that fast section of the route was reduced in 2011, lengthening the typical end-to-end travel time from two hours flat to 2 hours and 17 minutes. Today, the $820 million service is planned to have eight daily round-trips with six total stops: Minneapolis, Coon Rapids, Cambridge, Hinckley, and Duluth in Minnesota, plus Duluth's twin port of Superior, Wisconsin.
One of the first comments I got after posting a link to the EA last week was a question: "Why do we need an environmental assessment to run a daily passenger train to Duluth over existing tracks?"
That's a good one to ask, and I don't have a very good answer. The route has existed for well over a century, and passenger trains ran on the line until 1985, so it's worth asking why something that is partially a restoration of former service should require an extensive environmental process. However, the proposal does push beyond the historical level of service considerably. A full history may reveal more, but this 1951 timetable shows just two daily round-trips along the route, plus another three on parallel railroads (both of which have seen major chunks of the route abandoned). In order to achieve eight round-trips a day and to allow faster speeds, a new parallel track is planned for 41 miles between Isanti and Hinckley. Most of the rest of the route would be limited to speeds of 79 or 90 mph, while this new segment of double-tracking (where there has historically only been a single track), will be the section dedicated to 110-mph operation.
Some other shorter segments of additional track will be installed in Minneapolis, between Fridley and Coon Rapids, and on the northern end in Superior. However, all of these are expected to fit within the original right-of-way granted to the railroad in the 19th century. There is certainly some call for the Environmental Assessment, though it shouldn't be treated any more significantly than a typical highway widening. Ultimately I'll answer the question with a question: Was the Northern Lights Express put through any more hoops than a project to add lanes to a freeway? If this review was more complicated than that, then some priorities need to get straightened out.
Another comment I received related to the pace of construction for the route. Wouldn't it be better to start out with one or two trains a day and then scale it up incrementally?
That has certainly been considered, but there are many examples from around the country which show that incremental builds take ages to complete. Among the dozens of routes Amtrak operates nationally, only a handful of corridors have 8 or more daily round-trips today, a level of service that would be considered modest in Europe.
In the Northeast, only the Northeast Corridor from Boston to Washington, DC and branches off of it from New York to Albany, Philadelphia to Harrisburg, and DC to Richmond have 8+ daily round-trips. In the whole rest of the country, only two other corridors in California do as well: Los Angeles to San Diego, and Sacramento to Oakland.
View map
A few other routes have five to seven trains each direction each day. Why should a route to a relatively minor metropolitan area of 280,000 people be at the same level as these major corridors? Another very good question. There really should be many corridors across the country that see that much passenger train traffic or more. This route is also planned to have an average end-to-end speed of 67 miles per hour, and there's only one route anywhere in the U.S. running faster than that today: The Acela Express from Washington, DC to Boston. Everything else falls in the range of 38 to 57 mph.
The NLX planners used computer models of ridership to come up with the speed and frequency of service. The models told them that this speed and number of trips are the bare minimum needed in order to operate the trains without a direct subsidy year over year. 67 mph is just barely faster than a typical driver will do over a whole trip (keep in mind that Interstate 35 has a 70 mph speed limit for most of its length between Duluth and the Twin Cities—most drivers will have top speeds reaching or exceed that, but any stops or slowdowns along the way will cause average speed to drop rapidly).
When costs are spread out across the number of passengers who will use the service over time, it also works out pretty well. A typical Amtrak short-distance "corridor" route requires an operating subsidy of $20 for every 100 passenger-miles traveled, the projected average trip length for NLX passengers. Existing corridor trains have periodic needs for additional capital costs as well. The Northern Lights Express is expected to start out carrying over 900,000 passengers in early years, and slowly but steadily growing from there. Over the next 30 years, that probably translates to 33 to 40 million passengers. If the project can achieve what the computer models say and operate without significant subsidies, the capital cost per rider would work out to somewhere between $20 and $25 for that time span.
So you can start out with a slow, infrequent train and pay half the cost of each rider's trip in order to entice them to use the service, or an up-front investment can be made to improve travel times and add frequency, and the overall cost works out to be about the same—potentially better in some cases. If we went with an incremental approach, there would be years and years worth of direct operating subsidies, plus the capital investment would probably work out to just as much as what's currently planned.
While the initial price tag is certainly giving some of our state politicians heartburn, in the long run, it works out better to invest in the route now.
Friday, March 15, 2013
Inducing demand for sustainability
The idea of induced demand is a strange one. You would think that building a highway or widening a road would alleviate congestion by spreading out the existing traffic across more space, and that would be the end of it. Toss in a little extra width in anticipation of population growth, and it should be possible to leave it alone for several decades, right?
In reality, new and expanded highways tend to see traffic counts rocket upward and approach full capacity in just a few short years. Highways can pull traffic from nearby low-speed streets and also practically create demand out of thin air. When new trip opportunities open up, people take them. New destinations become reachable, which drives more traffic, which drives more businesses and people to locate out along the highway, continuing the dizzying spiral. This cycle has motivated a lot of economic activity across the country, but it has caused a great deal of damage to our environment in terms of pollution as well as dramatically altered landscapes. In many ways, our culture has shifted from being freed by car ownership to being shackled by it. Most American cities only have tiny areas in them where it's possible to go about doing everyday tasks on foot, by bike, or on public transit without spending inordinate amounts of time doing so.
The country has spent about 90 years first building out a basic highway network, and then overlaying freeways on top of that a few decades later. Today, car-based travel retains a huge advantage over every other way of getting around the vast majority of the time. Despite that, there are small pockets showing that it is possible to dethrone the car as the king of the mountain, though it's harrowing to ponder whether alternatives can scale up fast enough to help us prevent the planet from melting.
Cities across the country have watched bicycle ridership boom as new bikeways are added, whether they are traffic-calmed neighborhood streets, new bike lanes on busier thoroughfares, or dedicated infrastructure. Use of public transportation has also been growing rapidly in recent years, with 2012 reported as the second-busiest year for urban mass transit since 1957. Amtrak has been setting ridership records constantly, more than doubling ridership since the railroad's introduction in 1971. Of course, the country has grown in population by 100 million since 1971, and far more since '57, so there's still a long way for them to climb.
Some transit systems around the world have been dealing with continuing growth straining their systems for decades. The London Underground comes to mind as one—in recent years, the system has been so crowded in central areas that kiosks with maps and other wayfinding information have been installed above-ground to encourage people to walk rather than ride the rails to their destination.
Meanwhile, the TGV network in France has shown that it's possible to operate trains profitably at high speed while offering very low fares. While most other high-speed services have marketed fast trains as a premium service, France has pivoted in the opposite direction by making them cheap to encourage their use over slow, meandering classic routes that had been congested with passengers hopping between small cities and towns. Recently, the "OuiGo" service was introduced with fares starting as low as €10 and maxing out at around 85 for a 500-mile journey. With a range of $0.02 to $0.17 per mile, it's extremely cheap—the low-end fare is as low or lower than what it would cost to simply provide power (fuel) to an electric car over such a trip, not counting wear-and-tear or other operating costs.
Of course, one of the TGV network's tricks has been to progressively increase the capacity of their trains over time. Individual bilevel TGV Duplex trains carry more than 500 passengers each, and two trains are often coupled together to have a capacity over 1,000. The trains used in OuiGo service bump that up to around 1200 by converting café cars into more seating space. So if you have 1,200 passengers, it's possible to get by with razor-thin profit margins per seat.
At such prices, the French rail operator SNCF is most certainly inducing travel demand that would otherwise not exist. One could ask, have they gone too far? That's a question for the age, isn't it? Of course, high-speed trains run on electricity and French ones primarily get power from nuclear plants, so these new riders probably aren't making much of a dent with CO2 emissions, but there could be other effects such as the depopulation of small towns away from the high-speed network in favor of others that lie directly on it.
Back here in the U.S., Amtrak tends to charge high fares on busier corridors with higher service frequency, while charging less for quieter ones. And the only high-speed train in the country, the Acela Express, seems to get a price category all of its own. Long-distance trains are mostly priced in the $0.15 to $0.20/mi range, with shorter-distance "corridor" trains ranging from $0.20 to $0.45/mi. The Acela tips the scales with an average fare of $0.78/mi, probably at least eight times the average OuiGo fare. But even here, we can see the effect of lower fares on ridership.
In the above graph, I plotted passenger-miles versus train-miles, with color indicating frequency of service, and the size of the circle showing the average fare per passenger-mile. It always amazes me that the Empire Builder does so well in terms of ridership when it runs through the sparsely-populated states of North Dakota, Montana, and Idaho on its way to the Pacific Northwest. It was ranked 3rd in terms of passenger-miles according to the FY2011 data I used, trailing only the Northeast Regional and Acela Express on that measure (for clarity of other routes, they have been cropped out of the graph).
Now why would the Empire Builder do as well as it does? Part of it is just that the train goes a long distance and has many places to pick up and drop off passengers along the way, but there are other long-distance routes in the system that go just about as far and hit far more well-populated areas. That remains something of a mystery to me, though there are a few other points in its favor. The Empire Builder is also really two or three trains in one, branching into two parts to reach both Portland and Seattle, plus often gaining an extra car on the leg between Saint Paul and Chicago. Looking at this plot of data, it also seems that cheap fares could attract many people who would otherwise stay away.
Perversely, one of the major outliers in this graph is the Auto Train, an oddball non-stop service between the D.C. suburbs and Florida which lets passengers bring their car along. Even when Americans ride trains, we are enticed by new ways to move our cars around.
Anyway, could Amtrak benefit from flipping their current pricing model on its head and driving down costs on its popular services rather than ramping them up further and further? It sure seems like many higher-cost routes have suppressed passenger demand. It might work in some cases, but Amtrak has always been hamstrung by an inflexible route network and fleet of rolling stock. There simply isn't the equipment to duplicate the French model of dumping 1,000 or more passengers into a single train and sending it down the track. The Acela has been stuck with a fixed seating arrangement carrying barely more than 300 passengers at a time. Amtrak also hasn't been able to benefit from a fresh new network of high-quality lines built with good levels of cost control. Rather, the railroad has been saddled for decades with aging equipment and routes in need of maintenance. Efforts to remake the railroad have always come in fits and starts, without the sustained cohesive planning and funding necessary to really make it work the way it should.
Of course, one thing that is true about the French rail network is that the track owner (RFF) raises prices for whole trains as routes get busier, but SNCF (the company operating the rolling stock) has done what they can to use economy of scale to drive down costs for individual passengers. It'll be interesting to see if they can continue the process in the years to come, or if the commoditification of travel will finally hit a wall at some point.
Zooming back out (or perhaps back in) to look at other ways of getting around, urban mass transit may have similar forces at play compared to what drives railroad ridership. Even though our regional bus network has rush-hour fares of $2.25 for local buses and $3.00 for express, many people balk at paying that price to get to work or other destinations around town. It's not all that much—you can make it to work and back for less than the price of a medium dark chocolate mocha at the local coffee shop. But still, when overall transit ridership remains relatively low, why don't agencies simply look at reducing fares or even eliminating them in order to attract more people?
Well, we do have a couple local examples of that happening. The Northstar commuter line had fares reduced last year, and reports are that it has had a strongly positive impact on the number of passengers carried. Of course, the fare reduction was also accompanied by a targeted advertising blitz and the opening of an additional station in Ramsey, so there was probably a combination of things going on there. At the University of Minnesota, the campus has been running a free-fare bus service for students for at least 15 years now. It's the second-busiest transit system in the state, so they must have done something right. But service frequencies dropping as low as a minute or so apart, some would argue that it's too nice of a service to have. Students are highly opportunistic in their use of the campus shuttles, and will sometimes take them even if it doesn't really save any time when compared with walking.
For motorized transportation of various kinds, we know that use can scale up almost 1:1 with capacity, particularly if the cost to use the system is free or nearly free. At a certain point, it becomes necessary to start diverting or suppressing traffic by adding costs, or adding barriers of sorts, such as intentionally slowing things down or reducing service. But as congestion gets monetized, it's also important to make sure that the cash flow doesn't become an incentive to overbuild.
And before I wrap up, it's important to note that walking and biking, which are extremely cheap and have essentially no carbon footprint, should be prioritized highest of all in our ways of getting around. Both have been extremely neglected over the last century. Now, that doesn't necessarily mean building sidewalks everywhere or continuing to rip out rail infrastructure in order to build new bike trails, but it does mean that planners should always be thinking with their feet. How will this new development face the street? Will the design reinforce our human curiosity and make it an interesting place to walk or bike past, or will it silently push people away with blank walls and dull tones? Do our streets and rail lines have safe ways for people to get across?
The current generation has to work on flipping our transportation system upside-down, not to mention retrofitting our massive inventory of buildings, in order to find the efficiencies needed in order to keep climate change at bay. Finding a true balance between need, desire, and sustainability is the challenge. It will require new ways of thinking, but it can be done.
In reality, new and expanded highways tend to see traffic counts rocket upward and approach full capacity in just a few short years. Highways can pull traffic from nearby low-speed streets and also practically create demand out of thin air. When new trip opportunities open up, people take them. New destinations become reachable, which drives more traffic, which drives more businesses and people to locate out along the highway, continuing the dizzying spiral. This cycle has motivated a lot of economic activity across the country, but it has caused a great deal of damage to our environment in terms of pollution as well as dramatically altered landscapes. In many ways, our culture has shifted from being freed by car ownership to being shackled by it. Most American cities only have tiny areas in them where it's possible to go about doing everyday tasks on foot, by bike, or on public transit without spending inordinate amounts of time doing so.
The country has spent about 90 years first building out a basic highway network, and then overlaying freeways on top of that a few decades later. Today, car-based travel retains a huge advantage over every other way of getting around the vast majority of the time. Despite that, there are small pockets showing that it is possible to dethrone the car as the king of the mountain, though it's harrowing to ponder whether alternatives can scale up fast enough to help us prevent the planet from melting.
Cities across the country have watched bicycle ridership boom as new bikeways are added, whether they are traffic-calmed neighborhood streets, new bike lanes on busier thoroughfares, or dedicated infrastructure. Use of public transportation has also been growing rapidly in recent years, with 2012 reported as the second-busiest year for urban mass transit since 1957. Amtrak has been setting ridership records constantly, more than doubling ridership since the railroad's introduction in 1971. Of course, the country has grown in population by 100 million since 1971, and far more since '57, so there's still a long way for them to climb.
Some transit systems around the world have been dealing with continuing growth straining their systems for decades. The London Underground comes to mind as one—in recent years, the system has been so crowded in central areas that kiosks with maps and other wayfinding information have been installed above-ground to encourage people to walk rather than ride the rails to their destination.
Meanwhile, the TGV network in France has shown that it's possible to operate trains profitably at high speed while offering very low fares. While most other high-speed services have marketed fast trains as a premium service, France has pivoted in the opposite direction by making them cheap to encourage their use over slow, meandering classic routes that had been congested with passengers hopping between small cities and towns. Recently, the "OuiGo" service was introduced with fares starting as low as €10 and maxing out at around 85 for a 500-mile journey. With a range of $0.02 to $0.17 per mile, it's extremely cheap—the low-end fare is as low or lower than what it would cost to simply provide power (fuel) to an electric car over such a trip, not counting wear-and-tear or other operating costs.
Of course, one of the TGV network's tricks has been to progressively increase the capacity of their trains over time. Individual bilevel TGV Duplex trains carry more than 500 passengers each, and two trains are often coupled together to have a capacity over 1,000. The trains used in OuiGo service bump that up to around 1200 by converting café cars into more seating space. So if you have 1,200 passengers, it's possible to get by with razor-thin profit margins per seat.
At such prices, the French rail operator SNCF is most certainly inducing travel demand that would otherwise not exist. One could ask, have they gone too far? That's a question for the age, isn't it? Of course, high-speed trains run on electricity and French ones primarily get power from nuclear plants, so these new riders probably aren't making much of a dent with CO2 emissions, but there could be other effects such as the depopulation of small towns away from the high-speed network in favor of others that lie directly on it.
Back here in the U.S., Amtrak tends to charge high fares on busier corridors with higher service frequency, while charging less for quieter ones. And the only high-speed train in the country, the Acela Express, seems to get a price category all of its own. Long-distance trains are mostly priced in the $0.15 to $0.20/mi range, with shorter-distance "corridor" trains ranging from $0.20 to $0.45/mi. The Acela tips the scales with an average fare of $0.78/mi, probably at least eight times the average OuiGo fare. But even here, we can see the effect of lower fares on ridership.
In the above graph, I plotted passenger-miles versus train-miles, with color indicating frequency of service, and the size of the circle showing the average fare per passenger-mile. It always amazes me that the Empire Builder does so well in terms of ridership when it runs through the sparsely-populated states of North Dakota, Montana, and Idaho on its way to the Pacific Northwest. It was ranked 3rd in terms of passenger-miles according to the FY2011 data I used, trailing only the Northeast Regional and Acela Express on that measure (for clarity of other routes, they have been cropped out of the graph).
Now why would the Empire Builder do as well as it does? Part of it is just that the train goes a long distance and has many places to pick up and drop off passengers along the way, but there are other long-distance routes in the system that go just about as far and hit far more well-populated areas. That remains something of a mystery to me, though there are a few other points in its favor. The Empire Builder is also really two or three trains in one, branching into two parts to reach both Portland and Seattle, plus often gaining an extra car on the leg between Saint Paul and Chicago. Looking at this plot of data, it also seems that cheap fares could attract many people who would otherwise stay away.
Perversely, one of the major outliers in this graph is the Auto Train, an oddball non-stop service between the D.C. suburbs and Florida which lets passengers bring their car along. Even when Americans ride trains, we are enticed by new ways to move our cars around.
Anyway, could Amtrak benefit from flipping their current pricing model on its head and driving down costs on its popular services rather than ramping them up further and further? It sure seems like many higher-cost routes have suppressed passenger demand. It might work in some cases, but Amtrak has always been hamstrung by an inflexible route network and fleet of rolling stock. There simply isn't the equipment to duplicate the French model of dumping 1,000 or more passengers into a single train and sending it down the track. The Acela has been stuck with a fixed seating arrangement carrying barely more than 300 passengers at a time. Amtrak also hasn't been able to benefit from a fresh new network of high-quality lines built with good levels of cost control. Rather, the railroad has been saddled for decades with aging equipment and routes in need of maintenance. Efforts to remake the railroad have always come in fits and starts, without the sustained cohesive planning and funding necessary to really make it work the way it should.
Of course, one thing that is true about the French rail network is that the track owner (RFF) raises prices for whole trains as routes get busier, but SNCF (the company operating the rolling stock) has done what they can to use economy of scale to drive down costs for individual passengers. It'll be interesting to see if they can continue the process in the years to come, or if the commoditification of travel will finally hit a wall at some point.
Zooming back out (or perhaps back in) to look at other ways of getting around, urban mass transit may have similar forces at play compared to what drives railroad ridership. Even though our regional bus network has rush-hour fares of $2.25 for local buses and $3.00 for express, many people balk at paying that price to get to work or other destinations around town. It's not all that much—you can make it to work and back for less than the price of a medium dark chocolate mocha at the local coffee shop. But still, when overall transit ridership remains relatively low, why don't agencies simply look at reducing fares or even eliminating them in order to attract more people?
Well, we do have a couple local examples of that happening. The Northstar commuter line had fares reduced last year, and reports are that it has had a strongly positive impact on the number of passengers carried. Of course, the fare reduction was also accompanied by a targeted advertising blitz and the opening of an additional station in Ramsey, so there was probably a combination of things going on there. At the University of Minnesota, the campus has been running a free-fare bus service for students for at least 15 years now. It's the second-busiest transit system in the state, so they must have done something right. But service frequencies dropping as low as a minute or so apart, some would argue that it's too nice of a service to have. Students are highly opportunistic in their use of the campus shuttles, and will sometimes take them even if it doesn't really save any time when compared with walking.
For motorized transportation of various kinds, we know that use can scale up almost 1:1 with capacity, particularly if the cost to use the system is free or nearly free. At a certain point, it becomes necessary to start diverting or suppressing traffic by adding costs, or adding barriers of sorts, such as intentionally slowing things down or reducing service. But as congestion gets monetized, it's also important to make sure that the cash flow doesn't become an incentive to overbuild.
And before I wrap up, it's important to note that walking and biking, which are extremely cheap and have essentially no carbon footprint, should be prioritized highest of all in our ways of getting around. Both have been extremely neglected over the last century. Now, that doesn't necessarily mean building sidewalks everywhere or continuing to rip out rail infrastructure in order to build new bike trails, but it does mean that planners should always be thinking with their feet. How will this new development face the street? Will the design reinforce our human curiosity and make it an interesting place to walk or bike past, or will it silently push people away with blank walls and dull tones? Do our streets and rail lines have safe ways for people to get across?
The current generation has to work on flipping our transportation system upside-down, not to mention retrofitting our massive inventory of buildings, in order to find the efficiencies needed in order to keep climate change at bay. Finding a true balance between need, desire, and sustainability is the challenge. It will require new ways of thinking, but it can be done.
Monday, March 4, 2013
How (not) to fill a train
I wrote a simple Python script to simulate customers attempting to book passage on a 100-seat train making journeys of anywhere between two stops and 40 stops (each number of stops was simulated 20 times). Each customer chose a random start and end point for their journey. Seats are filled on a first-come, first-served basis: The first passenger always gets seat "0". As each customer comes along, the program checks to see if seat "0" is occupied for any portion of the planned trip. If it is, then the program moves on to seat "1". The process repeats as necessary until the list of seats is exhausted. I set up the program so that 500 attempts would be made for every test—for a stop count of 2, 100 passengers were able to get seats, but 400 other customers were rejected.
That's a very simplistic algorithm which doesn't work very well. It becomes difficult to add more passengers after just 5 stops. Amtrak does better than this, though it's also worth noting that Amtrak reservations are typically on a per-car basis rather than per-seat (per-seat was more straightforward for me to model), so some of the seat conflicts are resolved naturally.
There are a lot of computer performance graphs out there which look exactly like this. In particular, I think of multi-processor systems of yore (i.e., 10–15 years ago). Today, well-written software is much better at scaling almost linearly with the number of processor cores. Some better scheduling software would probably help Amtrak on routes with many stops, but unlike computer programs, people can't be moved around in the same ways.
Here are graphs using both a normal and log scale for the number of stops:
That's a very simplistic algorithm which doesn't work very well. It becomes difficult to add more passengers after just 5 stops. Amtrak does better than this, though it's also worth noting that Amtrak reservations are typically on a per-car basis rather than per-seat (per-seat was more straightforward for me to model), so some of the seat conflicts are resolved naturally.
There are a lot of computer performance graphs out there which look exactly like this. In particular, I think of multi-processor systems of yore (i.e., 10–15 years ago). Today, well-written software is much better at scaling almost linearly with the number of processor cores. Some better scheduling software would probably help Amtrak on routes with many stops, but unlike computer programs, people can't be moved around in the same ways.
Here are graphs using both a normal and log scale for the number of stops:
How distance matters: A map and two charts
I've made a couple of aborted attempts at ranting at the Brookings Institution's Amtrak report published on Friday. Instead, I'll just post some graphs I made from their data which seemed interesting.
On Amtrak routes, ridership per train appears to scale with the log of distance. Ridership continues to rise as route length increases, though the rate of increase drops off as routes get longer. Shorter routes tend to have higher frequency of service and more closely-spaced stations. The longest routes also go through some of the least-populous areas of the country (western states). Of course, the sparseness of population doesn't explain why the Empire Builder is the most-ridden long-distance route. The fact that it's basically two (or even three) trains in one might, though.
First, I'll toss in my map of Amtrak station ridership across the country, since I haven't posted about it yet (I still have to work on describing it better at some point):
Now here is ridership per train (annual ridership divided by trains per year) versus distance (log scale), with the size of the circle showing riders per train-mile. Circles are colored according to frequency of service.
This graph plots riders per train-mile versus distance (log scale on both axes), with riders per train as the circle size. Also colored according to frequency of service.
There's a common statement in rail punditry that 400 miles is the limit for viable service, and it's often stated as though ridership suddenly drops off a cliff at that point. I suspect the 400-mile distance really has more to do with political and geographical boundaries. Within the U.S., individual states are often 200 to 400 miles across. In Europe, the Mediterranean Sea is about 400 miles away from Paris.
Anyway, these graphs also indirectly show that ridership scales more or less linearly with frequency of service -- add a second train, and you should expect roughly twice the ridership. So one question worth asking is whether operational costs scale linearly with frequency of service or not.
I'll note that I mostly used frequency of service from Brookings' report. Frequency and route length both become a bit fuzzy since some corridors will only have trains run for part of the distance. I've also noted in the past that Amtrak counts "corridor" trains as Northeast Regionals for the distance they run in the NEC. So the Regional's numbers are probably inflated, while corridor train numbers are deflated (such as the Vermonter). I haven't tried to compensate for that in these graphs. My only change to Brookings data was to tweak the frequencies for the thrice-weekly Sunset Limited and Cardinal and the quad-weekly Hoosier State.
On Amtrak routes, ridership per train appears to scale with the log of distance. Ridership continues to rise as route length increases, though the rate of increase drops off as routes get longer. Shorter routes tend to have higher frequency of service and more closely-spaced stations. The longest routes also go through some of the least-populous areas of the country (western states). Of course, the sparseness of population doesn't explain why the Empire Builder is the most-ridden long-distance route. The fact that it's basically two (or even three) trains in one might, though.
First, I'll toss in my map of Amtrak station ridership across the country, since I haven't posted about it yet (I still have to work on describing it better at some point):
Now here is ridership per train (annual ridership divided by trains per year) versus distance (log scale), with the size of the circle showing riders per train-mile. Circles are colored according to frequency of service.
This graph plots riders per train-mile versus distance (log scale on both axes), with riders per train as the circle size. Also colored according to frequency of service.
There's a common statement in rail punditry that 400 miles is the limit for viable service, and it's often stated as though ridership suddenly drops off a cliff at that point. I suspect the 400-mile distance really has more to do with political and geographical boundaries. Within the U.S., individual states are often 200 to 400 miles across. In Europe, the Mediterranean Sea is about 400 miles away from Paris.
Anyway, these graphs also indirectly show that ridership scales more or less linearly with frequency of service -- add a second train, and you should expect roughly twice the ridership. So one question worth asking is whether operational costs scale linearly with frequency of service or not.
I'll note that I mostly used frequency of service from Brookings' report. Frequency and route length both become a bit fuzzy since some corridors will only have trains run for part of the distance. I've also noted in the past that Amtrak counts "corridor" trains as Northeast Regionals for the distance they run in the NEC. So the Regional's numbers are probably inflated, while corridor train numbers are deflated (such as the Vermonter). I haven't tried to compensate for that in these graphs. My only change to Brookings data was to tweak the frequencies for the thrice-weekly Sunset Limited and Cardinal and the quad-weekly Hoosier State.
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