Photo by the author.

On Monday, entrepreneur Elon Musk announced plans to build

a design for a super-fast tube train connecting Los Angeles and San Francisco. He believes his plan will obviate the need for the California High-Speed Rail. Unfortunately, his math doesn’t add up.

The “Hyperloop” would be a pair of tubes stretching from Los Angeles to the Bay Area. Pods within these tubes would travel at up to 760 mph, making the trip between California’s largest metro areas in 35 minutes. Musk says he became motivated to invent this technology because he grew disenchanted with the California High-Speed Rail project’s expense ($53 billion in 2013 dollars) and sloth (it will travel at an average of 168 mph).

Musk claims the Hyperloop system could be built for just $6 billion, 10% of the cost of HSR. Some are wondering if this is a serious proposal or a ploy intended to derail the California High-Speed Rail project. Evidence seems to point to the latter. After all, the guy proposing this revolution in transit owns a car company.

The Hyperloop concept has gotten a lot of press over the past few days. It seems to have inspired the masses like an idea out of Popular Mechanics. And it may very well be possible to build a system much like this one. Perhaps one day in my lifetime, people will be taking Hyperloops all over the nation.

Hyperloop concept drawings. All images from Musk’s proposal.

Let’s set aside for the moment any discussion of the technical feasibility of this project. The Hyperloop may very well be something that we have the skills and know-how to build. It may even be desirable in some corridors. But the technological concept is only part of what Musk has proposed.

Musk suggests that for less than 10% of the cost of building the long-planned high-speed rail line between Los Angeles and San Francisco, we can invent and build an entirely new technology. But the Hyperloop doesn’t actually make it to downtown LA or downtown San Francisco. It also has a maximum passenger capacity of just 10% of the HSR line. And it bypasses all of the intermediate population centers in central California that HSR will serve.

If it sounds too good to be true, you should probably double-check the math. And the math surrounding the Hyperloop definitely has problems.

Unrealistic promises?

According to Musk, pods would depart LA and San Francisco every 30 seconds during peak periods. Each pod can carry 28 passengers. That means that under the maximum throughput, the Hyperloop is capable of carrying 3,360 passengers each hour in each direction.

For context, a freeway lane can carry 2,000 cars per hour. A subway running at 3 minute headways (like the WMATA Red Line) can carry 36,000 passengers per hour. The California High Speed Rail, which this project is supposed to replace, will have a capacity of 12,000 passengers per hour.

That means that Musk’s proposal can carry only 20-25% of the passengers of the California High-Speed Rail under ideal circumstances. But are those ideal circumstances reasonable? Probably not.

The Hyperloop pods will travel at up to 760 miles per hour, just under the speed of sound, with pods traveling about 30 seconds apart in the tube. They will have a maximum deceleration of 0.5 gs, which is equivalent to 10.9 mph per second. At that rate of braking, it will take a pod 68.4 seconds to come to a full stop.

That’s a pretty significant issue because safe vehicle operation means never getting closer to the vehicle ahead than the distance it will take you to stop. If pod A were to experience a catastrophic air-skid failure, crash into the tube wall, and disintegrate, pod B, 30 seconds back, would not be able to stop short of the wreckage. In fact, pod C would also likely hit the wreckage of pods A and B.

That means that the minimum separation between pods is probably closer to 80 seconds or more. Not a big deal. It still means 45 departures per hour. But that’s only 1,260 passengers per hour in capacity. That’s 10% of what the California High-Speed Rail can carry.

With a capacity of 1,260 passengers per tube, that means that the Hyperloop would need 10 tubes in each direction (not 1) to move the same number of passengers as the proposed high-speed line. And that would push the cost up by 10, which is actually more than the cost of the HSR.

Limitations

The maximum throughput of a transit line equals the throughput of the segment with the least capacity. Simply put, if we have a 2-track railway that has a long single-track segment, the whole line is limited by that section.

The Hyperloop will have chokepoints, too. Because the tubes will be kept at a near-vacuum, each station will have an airlock that trains pass through. Every time a pod arrives, it has to decelerate and stop. Then the airlock will have to close, pressurize, and open again. Then the pod has to clear the airlock. Then the airlock can close, depressurize, and then reopen.

A Hyperloop pod at a station.

All of that has to happen in less than 30 seconds (if Musk is to be believed) or 80 seconds if vehicles are kept a safe distance apart.

Meanwhile, Musk says that each station can have 3 pods on the platform at once. If pods arrive every 30 seconds, then passengers and baggage have to get off within 60 seconds. One arthritic passenger or a guy who goes back for the iPhone he left behind, and pods start backing up in the tube.

So clearly, Musk needs to rethink headways. The 30-second headway isn’t feasible, meaning that his capacity will be significantly lower than he claims.

Maybe he can resolve that by using larger pods. But of course, a larger pod will weigh more. And that will probably mean using stronger steel for the tubes, which means that the cost will go up.

Apples to oranges

The California High-Speed Rail will whisk passengers from Los Angeles Union Station to the Transbay Terminal in downtown San Francisco in 2 hours and 48 minutes. That’s too slow for Musk, and he says the Hyperloop can get you from Los Angeles to San Francisco in 35 minutes.

Proposed Hyperloop route. The line would stop short of both Los Angeles and San Francisco.

But the Hyperloop won’t start in Los Angeles, and it won’t end in San Francisco. Instead, it’s proposed to start in Sylmar, 38 minutes north of Los Angeles Union Station aboard the Metrolink commuter train. That means it takes longer to get to the Hyperloop from downtown LA than it would take to go to San Francisco.

It’s unclear where the Hyperloop would end. Some maps show the line crossing the San Francisco Bay either on or adjacent to the Bay Bridge. But his cost projections don’t mention the expense of crossing the bay. Other maps show a terminal south of Oakland. So either his Bay Area station will be in the East Bay, requiring a transfer to BART to reach San Francisco, or he’s lowballing the cost of the project. The 11-year long effort to rebuild the eastern span of the Bay Bridge has cost $6.3 billion, so another crossing won’t be cheap.

Of course, there’s nothing technically infeasible about extending the Hyperloop into downtown LA or San Francisco. But it would significantly increase the costs of the project. The California High-Speed Rail’s sections in the San Joaquin Valley are also extremely cheap. If the HSR started in Sylmar and ended in Oakland, it would be significantly cheaper, too. While the cost of getting all the way downtown is already factored into the HSR project, it’s not part of the Hyperloop proposal.

Conclusions

Musk’s proposal won’t actually get riders to the downtowns of Los Angeles or San Francisco. It can only carry around 10% of the capacity of the California High-Speed Rail. Additionally, it will bypass other population centers, like Bakersfield, Fresno, and San Jose.

Building a truly workable Hyperloop, if it’s feasible at all, will be significantly more expensive than Musk claims. It might even be more expensive than the California HSR project. And Musk’s proposal leaves a lot of questions unanswered.

The Hyperloop would run atop an elevated structure.

How did he come to his construction cost estimate in the first place? Musk argues that the Hyperloop is cheaper than HSR because it’s elevated, saving on the cost of building at grade and reducing local opposition. But bridges are far more expensive than building tracks at grade. And just because the footprint is limited to a big pylon every 100 feet doesn’t mean that the environmental impact analysis process will be any easier or that the public will be any more receptive.

Other issues, like seismic stability, are simply glossed over. He claims that by elevating the Hyperloop tracks, they will be more stable than ground-running HSR. Clearly he’s unfamiliar with the Cypress Street Viaduct. That’s one reason that the California High-Speed Rail Authority insists on crossing all faults at grade.

Musk also claims that his giant steel tube will be okay with the only expansion joints at the Los Angeles and San Francisco ends. They’ll just be really big. That’s a significant engineering issue that cannot simply be ignored, at least not if Musk is in any way serious about this proposal.

Realistically, the Hyperloop is just hype. The concept might be technically feasible. But Mr. Musk’s proposal will cost a lot more and do a lot less than he claims it will. And clearly, it won’t replace the high-speed rail project he hates so much. But it might just sell some Teslas.