When California voters approved construction of a bullet train in 2008, they had a legal promise that passengers would be able to speed from Los Angeles to San Francisco in two hours and 40 minutes.

But over the next decade, the state rail authority made a series of political and financial compromises that slowed speeds on long stretches of the track.

The authority says it can still meet its trip time commitments, though not by much.

Computer simulations conducted this year by the authority, obtained by The Times under a public records act request, show the bullet train is three minutes and 10 seconds inside the legal mandate.

Such a tight margin of error has some disputing whether the rail network will regularly hit that two-hour-40 minute time, in part because the assumptions that went into those simulations are highly optimistic and unproven. The premise hinges on trains operating at higher speeds than virtually all the systems in Asia and Europe; human train operators consistently performing with the precision of a computer model; favorable deals on the use of tracks that the state doesn’t even own; and amicable decisions by federal safety regulators.

Frank Vacca, chief of rail operations for the California High-Speed Rail Authority, says the system will be “fully compliant” with the law and able to make the trip within the time limit in regular operations.

Speed is crucial to the project, and not just because of the legal mandate. Fast trains will directly affect ridership and revenue.

But speed doesn’t come cheap. Faster trains require costly longer tunnels and more viaducts. The price tag is $77 billion, up from the $33 billion when the project was approved.

State law does not give the project much room to maneuver.

The 2008 bond act approved by voters said the system had to be “designed to achieve” a trip time of two hours and 40 minutes. Rail authority officials have long contended that the legal fine print does not require them to actually operate trains on such a schedule. The interpretation raises the prospect that the state is spending billions of dollars on a capability it will never use.

“If they don’t get two hours and 40 minutes, they are not going to get the predicted benefits of this very expensive system,” said Daniel Brand, a retired ridership expert with Charles River Associates who conducted the early passenger studies for the project in the 1990s.

Vacca says it nonetheless makes sense: “You can have a car designed to go 150 miles per hour, but you don’t drive that fast.”

By international standards, the California timetable is audacious.

The Japanese Shinkansen operates between Tokyo and Osaka, a distance of 344 miles. The fastest trip takes two hours and 22 minutes, yielding an average speed of 145 mph, according to Japanese Railway schedules.

The French Train à Grande Vitesse, or TGV, operates the Paris-to-Lyon line over 243 miles and takes one hour and 59 minutes, according to TGV schedules. The average speed is 121 mph.

But the Los Angeles-to-San Francisco route, which would traverse three mountain ranges and five of the 10 largest cities in the state, is supposed to travel 438 miles in 2 hours and 40 minutes — requiring an average speed of 164 mph.

When the rail authority solicited international firms to help finance and build the system, the Spanish firm Sacyr Concesiones, which has helped build 40 bullet train systems around the world, warned the state in a 2015 report that “one of the main cost drivers is the requirement of 220-mph operating speed.”

“220 mph is higher than most if not all standard commercial speed for HSR,” the firm wrote.

Top speeds require precise track alignment — straight and level. Going over mountains requires deep tunnels so that the grades are half as steep as those on interstate freeways.

Quentin Kopp, chairman of the rail authority when the speed requirements were created in 2008, said the Legislature erred in trying to dictate train speeds.

“It does not make sense to run at these speeds given the cost, but it is too late to change,” said Kopp, a plaintiff in a suit alleging the state is violating the bond act. “You would have to go back to voters and they would turn it down as a way of stopping the project.”

Former California Treasurer William Lockyer, who was chief of the state Senate in 2008 and remains a supporter, says “these details of trip times may have been too specific, but that is easy to say now.”

The speed mandate was created by political staffers and bureaucrats huddled in a Senate conference room in 2008. They believed guaranteeing high speeds was crucial to the system and to persuading voters to back $9-billion in bonds that year.

The main proponent of mandating the trip times was Mehdi Morshed, the longtime chief executive of the rail authority who believes rail speeds would be endlessly compromised were they not backed up by law.

“High speed doesn’t mean much if you don’t put in the law that you will have to get from one place to another in a certain amount of time,” he said.

The law, however, has in some cases failed to prevent the kinds of compromises Morshed feared.

In 2011, the rail authority faced growing opposition in Silicon Valley about an elevated viaduct that would carry 220-mph trains. The state agreed to put the bullet train on ground-level tracks shared with slower commuter trains between San Jose and San Francisco. A similar compromise was later made between Burbank and Los Angeles.

In 2016, the rail authority cut costs by reducing the planned diameter of roughly 50 miles of mountain tunnels, which lowered speeds to a maximum of 200 mph. This year, the rail authority gave up plans for dedicated tracks over 30 miles from Gilroy to San Jose, saying it would try to build track on a freight right-of-way that would limit speeds to 110 mph.

Many transportation experts, including state staff and independent analysts, have long dismissed the probability that any operational California bullet train will meet its timetable. A state-appointed peer review panel warned the Legislature in 2013 that “it is unlikely that trains would actually be scheduled to run during normal hours of operation within … 2-hour, 40-minute limits.”

Brand, the retired ridership expert, echoes that: “It is not that they could never achieve it, but it would be very difficult to do.”

The computer simulations that are supposed to prove the validity of the trip times are based on a lot of hope.

One key assumption is that trains will move through the urban Bay Area and Los Angeles nonstop, even while sharing track with trains that make multiple stops at stations along the way.

It would involve using parallel tracks, which exist only along limited segments of rail, to bypass commuter trains, Vacca said. During rush hour, the puzzle would require as many as four bullet trains to weave around six commuter trains per hour relying on a new signaling system.

Caltrain commuter trains in the Bay Area may have to sit idle for up to seven minutes while bullet trains pass, according to a 2016 rail authority planning document prepared by a Swiss consultant. Caltrain officials said there is no agreement on such future movements on the track, which Caltrain owns.

The trains would also have to sail through Fresno, Bakersfield and other communities at 220 mph, speeds that have triggered a public backlash in Europe, said Lisa Schweitzer, a USC professor who specializes in transportation.

“I can’t imagine most communities would agree to trains operating at these speeds,” she said.

Vacca said any noise or vibration effects on communities would be mitigated through features such as sound walls.

Another key assumption is that trains on shared track would receive federal approval to pass through at-grade crossings in dense urban areas at 110 mph, requiring sophisticated gates to prevent crashes.

“It is possible to do 110 mph on some of the [highway] crossings, but it is a real challenge on the Caltrain corridor,” said Grady Cothen, a former Federal Railroad Administration safety chief and attorney.

“There are no safety issues,” Vacca, formerly Amtrak’s chief engineer, said. “I see no reason why we can’t.”

The computer simulations also assume trains would stop and start in San Francisco at a commuter rail station rather than the downtown Transbay terminal identified in the bond act as the system’s terminus. The authority would need to dig a curvy 1.3-mile train tunnel under the city to reach Transbay.

The train authority remains committed to drawing passengers from airlines — even though the route’s length is at the upper end of the range where rail can compete.

Robert Poole, a transportation expert at Reason Foundation, a libertarian nonprofit, notes that Florida is building its Brightline passenger rail system between Miami and Orlando at much lower cost and considerably lower speed. With a top speed of 125 mph, the aim is to divert motorists from highways rather than competing with airlines.

“It is a very clever design,” Poole said. “They figured three hours from Miami to Orlando was good enough.”

ralph.vartabedian@latimes.com

Twitter: @rvartabedian