Why high speed rail hasn’t caught on

High Speed Rail (HSR) has been in the news, with a recent New York Times article listing some of the reasons that the California HSR project seems unlikely to ever be completed. Quite aside from California’s development quagmire and the article’s author’s unstated involvement in the story, there are a series of much deeper, physical reasons why HSR hasn’t really caught on. I haven’t seen these developed in accessible blog form so I thought I would write this brief note on the topic.

[Edit: This blog generated more controversy than usual, and a thread on HN. I was surprised to see how readily some of the core ideas were misunderstood, though it is true that I haven’t written as much recently as I used to, and I’m almost certainly less sharp as a result. This blog contains generalizations and inaccuracies – it’s intended as a jumping off point for the interested reader. One of them (Ashton) wrote a rebuttal! The bottom line is that California high speed rail won’t work for dozens of reasons, and I wrote about a few relatively obscure but quite fundamental ones.]

My personal background on trains is that I love them! I’ve taken hundreds of trains across multiple timezones, in China, Japan, Mongolia, Russia, all over Europe, Vietnam, Cuba, Australia, New Zealand, and the US. I also worked on track-based transport as a levitation engineer at Hyperloop between 2015 and 2018, so I have some appreciation for the art. I also spent a bunch of time on transport economics at Hyperloop, which taught me a lot about why my frustrations with rail’s failure to take over actually occurred, as well as some of the deeper reasons why Hyperloop is a rather challenged idea. For those who want more depth, parts of this blog derive from academic studies on wheel-rail dynamic vibration and rail spalling, more rolling contact fatigue, and Japanese shinkansen maintenance analysis.

Despite my ongoing enthusiasm for HSR, I have to concede that it is not a universal panacea. It remains relatively niche and relatively undeveloped. It is possible that its failure to be deployed everywhere since it was first developed 50 years ago is due to short-sighted governments and cost disease (the tendency for modern construction within developed cities to cost much much more than the original project did historically), but other factors also contribute to its lack of competitiveness.

To illustrate this, let’s examine past and current HSR development.

Despite decades of development, only a handful of routes in Europe operate at anything like airplane-competitive speeds, which for all but the shortest routes, require > 300 km/h or > 185 mph.

Even turboprop aircraft, which are relatively slow, cruise at > 500 km/h, while jets cruise at > 800 km/h. Over longer routes, the relative hassle of getting to and from an airport instead of an HSR rail terminal is eroded by the higher speed of aircraft, even in places where the rail terminal is in a densely populated city center and the airport is way outside. Comfort and convenience are other important factors, but there aircraft are also quite competitive.

In general, the number of >300 km/h HSR networks on Earth can be counted on one hand, and the total track length is a minuscule and mostly static fraction of global rail network length, which itself is shrinking at a reasonably rapid pace.

Japan, a linear archipelago, famously developed the high speed Shinkansen but like recent Chinese development, it must be seen in the context of very heavy-handed government subsidies and a response to geographic and structural factors that inhibited the development of airports. For example, while the US has more than 15,000 airports (most of which are untowered paved strips), Japan and much of China is relatively mountainous, historically relatively poor, and historically beset by relatively poor transport networks. Add to that various Japanese prohibitions on certain weapons technology in the post war period and high speed rail served as a government imposed solution to mass transportation.

It did not come without cost, however. Japan’s ostensibly private rail companies have gone bankrupt and been bailed out so many times I’ve lost count, racking up billion dollar yearly deficits year after year. Indeed, as far as I know there isn’t a single HSR route anywhere on Earth that operates profitably on ticketing revenue, and so operation always requires substantial subsidies. I should probably mention here that actual ridership and thus fare revenue is, as a rule of thumb, typically around a third of the projections used to justify initial development.

One can argue that aviation and any other kind of transport also benefits from various subsidies, such as expenditure on the US Navy guaranteeing freedom of navigation, without which the global oil trade wouldn’t work. Or that CO2 emissions from aircraft are an unpriced externality that HSR partly alleviates. But if we care about HSR and its ability to enable people to travel with fewer emissions or lower costs, we need to understand why it’s so expensive, no matter who is building it or where.

Why is HSR so expensive?

I will discuss three main groups of reasons: rail is suboptimal, HSR grading requirements are really tough, and steel-on-steel rolling is less perfect than you might think.

Rail is kind of obsolete

The first set of reasons are common to all kinds of rail. As mentioned in my post on traffic congestion:

There are a few reasons. Some are similar to car economic problems, with peak and average demand variation, particularly for commuter services. But I think the fundamental reason is that compact diesel engines got, if not good, then acceptable, in the 1930s. After that, shippers could move freight in almost any form factor between any two points directly. Even in 2022, freight by rail is much slower as rail cars must wait in yards for trains to be assembled.

There is another direct issue with trains, which is that rail systems are, by their nature, one dimensional. Any disruption on a rail line shuts down the entire line, imposing high maintenance costs on an entire network to ensure reliable uptime. To add a destination to a network, an entire line must be graded and constructed from the existing network, and even then it will be direct to almost nowhere.

Contrast this with aircraft. There are 15,000 airports in the US. Any but the largest aircraft can fly to any of these airports. If I build another airport, I have added 15,000 potential connections to the network. If I build another rail terminal and branch line, at significantly greater cost than an airstrip, I have added only one additional connection to the network.

Roads and trucks are somewhere between rail and aircraft. The road network largely already exists everywhere, and there aren’t any strict gauge restrictions, mandatory union labor requirements, obscure signaling standards, or weird 19th century incompatible ownership structures. Damage or obstruction isn’t a showstopper, as trucks have two dimensions of freedom of movement, and can drive around an obstacle. In Los Angeles during the age of streetcars, a fire anywhere in the city would result in water hoses crossing the street from hydrant to firetruck, and then the network ground to a halt because steel wheels can’t cross a hose or surmount a temporary hump!

Building a metro system in an existing dense city is also great (if we can avoid cost disease) but for most of the cities in the US, the suburbs are already not walkable enough to enable non-vehicle transport to a neighborhood station. The suburbs of LA will never be able to depend on a Manhattan or Vienna-style underground railway.

To make this concrete in the context of the ill-fated California HSR project, the NYT article quotes the rail authority chair Tom Richards saying “The key to high-speed rail is to connect as many people as possible.” There are a couple of unstated assumptions here, but it also reveals a fundamental problem with California HSR as it was conceived, which is that in order to get enough political buy in it had to promise too many things to too many stakeholders.

If we want to reduce CO2-generating air traffic between San Francisco and Los Angeles (a worthy goal!) then the HSR route must be, above all, fast. The oft-stated goal time of 2 hours and 40 minutes is both unachievably rapid with finite money and current technology, and also too slow to compete with aircraft, but for insane TSA security delays that will probably also affect HSR. It prompted the Hyperloop experiment, which sidestepped some of the problems and generated others.

Routing HSR on the east side of the central valley via Bakersfield and Modesto means those cities can have a station, but frequent services means that most trains have to stop there, and each stop adds 20 minutes to the travel time just to slow down and speed back up. Alternatively, the stations and their railway corridors are extremely expensive city decorations that help no-one because the trains, dedicated to a high speed SF-LA shuttle, never stop. Because they are trains, we can’t have both. If it was aircraft, we could have smaller, more frequent commercial aircraft offering direct flights to dozens of destinations from both cities. But rail has relatively narrow limits in terms of train size and frequency meaning that any route will be both congested at peak times and under-utilized for much of the rest.

Serving peripheral population centers in California is a nice thing to do, but aircraft pollution from Modesto is not driving global warming. Car traffic from Modesto would hardly overwhelm the Interstate 5. HSR minimizes financial losses when it is serving large population centers with high speed direct services. By failing to make the political case serving the main mission, the CA HSR project adopted numerous unnecessary marginal requirements which added so much cost that the project is unlikely to succeed. Even if the money materializes and the project is completed, the train will be so slow that it will hardly impact aircraft demand, so expensive it will be unable to operate without substantial subsidies, and so limited in throughput that it will hardly even alleviate traffic from LA’s outer dormitory suburbs.

In other words, one can build a commuter rail network, an intercity network, or a point-to-point HSR line, but forcing all three usage modes into the same system cannot succeed.

The Earth is kinda bumpy

To understand the challenges of grading HSR, we need to first examine the nature of the bumpiness of the Earth.

To ancient humans who first walked the Earth, it appeared flat enough, at least at local scales. Go far enough or watch a Lunar eclipse and it becomes clear the Earth is, at large scale, round. To a decent approximation (about 0.3%) it is spherical.

Let’s examine corrections to this approximation. First, the equatorial bulge. The shape of the Earth is an equipotential, and centrifugal forces add to gravity, which makes the middle bulge out a bit – about 20 km depending on how one measures. There’s also some triaxiality, which is to say the equatorial bulge is marginally more bulgy through Africa/Hawaii than SE Asia/Americas. Next come the geoid corrections. Local variations in the density of the crust and upper mantle cause deviations to the equipotential surface of up to 100 m. This is rather small compared to the equatorial bulge, but still rather large. Once the geoid is added, we know everything there is to know about the Earth’s gravitational field, at least at scales of 100 km or so. Excepting deviations due to weather and tides of order 1 meter, the geoid gives the altitude of the ocean.

https://en.wikipedia.org/wiki/Geoid

The final layer of detail is hills, mountains, valleys, and other hard rocky stuff that pokes up on the Earth’s land surface. For essentially the entire world, this has been mapped to a resolution of 90 m by the Shuttle Radar Topography Mission, while substantial swaths of the US and other countries have been mapped to 1 m resolution or better, using airborne lidar.

Okay, the Earth has bumps. What’s the big deal?

The bumps have a really big effect on how fast people can move close to the surface of the Earth. There are two ways to understand this. The first is intuitively, and the second is by looking at the von Karman-Gabrielli diagram.

The force experienced due to bumps: F = m v^2/r. For a given curve of radius r, such as a hump in the road, the force experienced increases quadratically with velocity v. This is a big deal! The big deal, even!

Human passengers don’t like to experience high forces, especially while walking around in a train, so in practice this fundamental physical relation limits the r that can be experienced at a given v. For v = 320 km/h, r = ~8 km. This applies for both lateral and vertical deviations! For context, my children’s Brio train set has a radius of curvature of about 30 cm or 12″. 8 km is roughly the distance to the horizon.

This makes sense intuitively, too. A twisty road that is comfortable to drive at 35 mph is edgy at 45 and dangerous at 55 – where the forces are 2.5x greater! Walking through a crowded mall presents no challenge but sprinting is asking for trouble. Speed + bumps = trouble.

To a good approximation, HSR lines have to be dead straight. In Kansas or California’s central valley, this is fine, up to a constant in Eminent Domain, which is the politically fraught process of the government taking your land by force. But both LA and SF are ringed by a series of extremely geologically active, steep, and tall mountain ranges. The Interstate 5 out of LA goes through the Grapevine, passing through a point where 5 (5!!) different active fault lines intersect in one place. Maintaining a useful speed through these mountains, not to mention densely populated areas nearby, requires nearly 100 miles (!) of tunnels. Current tunneling costs are orders of magnitude too high, but even then tunnels are typically only built in places with known and acceptable geology, and much of the geology under the San Gabriel mountains is simply not known.

This is not the place to go into depth, but those mountains have seen things, geologically speaking, which should not be possible. What is known is that the entire mountain range is a gigantic pile of broken, crushed rocks that have been rotated, turned upside down, drowned, volcanically erupted, eroded, subducted, and then sheared. Just one of the dozens of tunnels required could easily cost more than $113b, the current estimated cost for the project.

From a 2015 article: “No way,” said Leon Silver, a Caltech geologist and a leading expert on the San Gabriel Mountains. “The range is far more complex than anything those people know.”

The mountains surrounding the Bay are not quite as tall but, straddling the San Andreas fault, no less challenging. Remember, at 320 km/h, anything taller than a viaduct standoff counts as a mountain that needs a cut or a tunnel – perhaps 20 meters of wiggle room if we’re being extremely generous.

The recent NYT article lists a bunch of political reasons that the project is in deep trouble but even if various CA governors and US presidents had written a Chinese-style blank check and there were no land acquisition disputes, the mountains are still there.

The second way to understand the bumpy earth limitation is the von Karman-Gabrielli diagram. This diagram plots the speed and specific power of every mode of transport on a single chart. I love this kind of data presentation.

The zeroth order truth of the vK-G diagram is that there is a limit line of vehicular performance, which is essentially determined by momentum transfer limitations for vehicles that have to displace water or air to move along. It does not apply to spacecraft!

The first order truth is that, above 100 mph, the most efficient transport mechanism shifts from ground-based to air-based. For smaller creatures than humans, the transition speed is a lot lower – most insects fly instead of walk. For insects, this is because at their scale, the world is ridiculously bumpy and hard to navigate.

The galaxy-brain detail is that, between 100 mph and 300 mph, there is a gap in the frontier, where no technology gets close to the G-K limit. Many innovators have tried to slot hovercrafts or ground effect vehicles (such as the ekranoplan) into this gap, but all have failed. Hovercrafts have not caught on for the same reason as HSR – above 100 mph, the Earth is too rough to travel close to its surface.

This is also intuitively obvious to pilots, who understand that making a habit of flying planes within 20 m (or even 200 m) of the surface, particularly in mountains, is a career-limiting move. Indeed, even at slower approach speeds, commercial airliners take half the city to turn around to line up with the runway. Translate the motion of a 737 on downwind, for example, to the surface and even a fighter pilot would not be able to track the ground within the range that HSR must be built.

As a result, HSR grades cannot be built between nearly any city pair on Earth without moving a LOT of dirt and rock and pouring a LOT of (CO2-emitting) concrete, most of which only has an actual train on it for a few seconds per hour, and thus drives incredibly high cost of construction.

Of course roads also operate with public subsidies and require expensive grading, but road traffic is slower, more diverse, and more versatile, while road materials are far cheaper and car operating costs are borne by the user. The result is that the per mile and per passenger mile costs of roads are much lower than HSR. For example, the I-70 cost an average of about $2m/mile, despite routing through remote and mountainous parts of Utah. CA HSR is currently budgeted at more than $350m/mile.

Rail wear, or steel wheels in the real world

Finally, we come to the third major challenge of HSR and another major contributor to its cost. Steel wheels and rails are hard – they’re made of steel, but they wear over time. Wheels must be remachined and rails must be reground.

A typical Japanese maintenance schedule has each segment of rail reground, to exacting tolerances, every 6 months while total replacement is required every 5 years. These grinding and replacement operations, which must be carried out continuously, degrade system up time and require, on average, a fully salaried track worker per km of track. These numbers apply only to perfectly straight track – switches, curves, and steep grades wear out substantially faster.

How does wear occur? A typical HSR wheel bears a static load of 6 T across a contact patch the size of a postage stamp, with both rail and wheel deforming about 20 microns to enable contact. The center of this patch endures a pressure high enough to plastically deform the rail’s steel! The passage of the wheel places symmetric forces (first forward, then back) but the effect is to temper the surface, which accumulates stresses and can flake off. Additionally, torque on the wheel tends to lock the wheel statically to the track as the patch is loaded, but during the unload portion as the wheel passes the accumulated stresses are released, resulting in shear and friction, particularly on parts of the track where the train is accelerating, slowing down, climbing, or descending.

Despite this terrifying pressure, one wheel passing might deform the surface by only a single Angstrom – the width of a single atom. The Tokaido Shinkansen sees 150 services a day, each with a 16 car train and 4 wheels per track per car, so the track endures 1.5 million wheels between 6-monthly regrindings. Linear damage would imply 0.15 mm of wear, but damage isn’t linear.

Instead, once the rails deform more than a few nanometers, the “bumpiness of the world” comes back with a vengeance. Bumps induce acoustic oscillations in the wheels and track, which ring like a gong or very angry violin. Wheels being made of hard steel, these oscillations are poorly damped and cause local variations in the position and force of the contact surface. Some of these variations cancel out the bumps and smooth out the tracks, but some of them don’t, and over time the randomness of these acoustic perturbations roughen the tracks by much more than a single layer of atoms per wheel.

Rail wheels are much lighter than the cars they support, so their suspension system drives them into the track with a force of about 700 gs. At 320 km/h, the critical r, or bump height, is just 50 microns. Less than the width of a hair, and not that different to the 20 micron (mostly) elastic deformation of the contact patch. Once acoustically grown bumps get to 5 microns or so, they begin to induce oscillations in the suspension system. This is damped better than the wheel’s acoustic modes, but damping always lags the input and the effect is to begin to drive “washboard” shapes into the rail, rapidly increasing track deformations. Once deformations exceed 50 microns, the wheel actually breaks contact with the track, hammering it on its return with almost unimaginable force and rapidly grinding out holes.

Cumulatively, these effects are at first linear over time, then quadratic, and eventually exponential. The forces are proportional to the square of velocity, so faster HSR trains damage rails faster. The Tokaido line averages around 140 mph (somewhat less than its peak of ~185 mph), but increase that speed by just 40% and rail lifetime will (at least) halve, while track maintenance costs (at least) double. Maintenance costs that were already on the order of $200,000/km/year, in 2003 dollars. That’s $400m/year just for rail maintenance for the LA-SF route, once we correct for inflation and a higher design speed.

There’s got to be an easier way

As of 2022, the CA HSR project is supposed to cost $113b. The vast majority of this is unfunded, and yet the final project will almost certainly cost at least 10x this if it ever completed, and will still be unable to compete on the LA-SF route with aircraft.

Similar stories abound the world over. There are a handful of locations where land is flat enough and property ownership protections weak enough that HSR can be built with minimal fuss, and sometimes even between cities with strong latent transport demand that can be unlocked, but even then it is a niche solution that takes decades to develop and can’t pay for itself. If this weren’t the case, we’d see HSR developed everywhere, instead of something governments talk about for decades and, usually, never actually build.

By CA HSR’s own numbers, the completed system may carry 35 million passengers per year by 2040, or 100,000 per day. This capacity could also be served by a fleet of just 40 737s (less than current LAX-SFO traffic), of which Boeing makes more than 500 per year. Bought new, this fleet would cost $3.6b, and with a lead time of, at most, a few months. Upgrades to Modesto and Bakersfield airport terminals could service the 737 for mere $10s of millions. The fleet would cost about $2.9b to operate each year, which under current airline business models can be served by fares of about $60 each way. If we operate this airline for free (no tickets!) for 40 years, the total operating costs climb to $120b, which is equivalent to CA HSR’s currently wildly unrealistic estimated construction costs.

That is, a passenger jet that first flew in 1967 can continue to profitably serve the LA-SF transportation market for less money, over multiple decades, than the rather slow HSR could be constructed much less operated, in our wildest dreams.

Where HSR has to bore tunnels through >100 miles of incredibly unforgiving hard and flakey rock for decades just to get somewhere, planes fly serenely through the unobstructed atmosphere. Where trains must slow down and speed up to serve political expediency in smaller intermediate stations, planes route freely through the three dimensional sky direct to their destination, and at 3x the speed, and at lower overall energy usage per passenger-km.

Planes emit CO2 as they fly, but CO2 emissions on routes that could be served by HSR are a tiny fraction of aviation’s total, which itself is a small fraction of the totality of humanity’s output. It can be directly offset through carbon capture and sequestration for a modest increase in the ticket price, as plane ticket prices are mostly not fuel. Alternatively, synthetic aviation fuel is under development to make aircraft carbon neutral. Indeed, at Terraform Industries we think synthetic fuel will ultimately be even cheaper than current options, expanding access to the convenience, speed, and safety of air travel.

Trains are wonderful and I love the Shinkansen, but let’s stop flogging this dead horse. HSR is not a compelling option for generic high speed intercity transport.