The Blend, HSR Style

The California High-Speed Rail Authority recently published a memo (requested by Kathy Hamilton and CARRD) justifying the oft-questioned claim that the Phase 1 "blended system" presented in the 2012 Business Plan is consistent with the trip-time requirements built into section 2704.09 of Proposition 1A, the HSR bond.  The trip times are in the bond language to prevent funds from being disbursed for projects that are not high-speed rail.

The memo states that the blended system will enable 30 minute non-stop trip times between San Francisco and San Jose.  In support of this claim, the memo provides the speed graph below, to which blue annotations have been added for clarification.  The annotations are necessary because the memo authors evidently did not go out of their way to explain the graph to non-engineers.

San Francisco to San Jose (southbound) speed versus distance graph, annotated.
Notches in the speed profile represent curve speed restrictions.

An independent calculation of the speed profile (using the output of a Train Performance Calculator that numerically integrates the differential equations of motion of the train, taking into account traction, braking, and drag forces) shows that an AGV train limited to 110 mph can travel from San Francisco 4th & King to San Jose in 33 minutes, under a slightly different set of assumptions where the train is slowed by a curve at Palo Alto, uses the existing 45 mph San Jose station approach, and makes an actual stop in San Jose.  After the differing assumptions are reconciled, the math does check out and the calculations are correct.

Those Pesky Assumptions

As for any computer simulation, the results are predicated on a set of input assumptions.  As the saying goes, "garbage in, garbage out"--bad assumptions will lead to bad results.  While the CHSRA's time of 30:22 is reasonable under the particular assumptions they made, the assumptions themselves are questionable.  They include:

1. The train starts from San Francisco 4th & King, not Transbay.  Starting from Transbay, with its notoriously slow approach, would add about another 3 minutes.
2. No Caltrain service is allowed for, or in their words, "Caltrain train service will allow for high-speed express train to run unimpeded between SF and SJ".  In Caltrain's blended operations analysis, all HSR services during rush hour make a two-minute stop at Millbrae, which has the effect of reducing the speed differential between HSR and Caltrain.  If HSR were to attempt a 30-minute run during rush hour, it is likely that Caltrain would be impacted by reduced rush hour track capacity, from six Caltrains per hour per direction to four or five.  The stop at Millbrae adds 3.5 minutes to the SF-SJ run.  Such is the nature of compromise.
3. No padding is included.  In the real world, timetables include a small amount of padding (5 to 7 percent) to allow for the occasional unplanned delay.  Over a half-hour SF - SJ run, a real-world timetable would add at least 1.5 minutes.
4. The train does not stop in San Jose, so no penalty is taken for the time lost as it slows down.  This alone is worth at least half a minute from 75 mph.
5. The train uses the least energy-efficient, pedal-to-the-metal driving style.  Brakes are applied fully and at the last moment, and acceleration is at full throttle.  In the real world, where energy and maintenance do cost money, a smoother and more energy-efficient traction and braking profile would add about 1 minute.
6. No speed restriction is present at Palo Alto, where a double reverse curve limits train speeds to 90 mph.  Slowing from 110 mph would add about 20 seconds.
7. The train approaches San Jose on an elevated viaduct leading into the proposed upper level at San Jose Diridon, maintaining a speed of 75 mph (as opposed to the slower 45 mph limit practiced on the existing alignment).
8. Timetables show departure times.  Departure from San Jose would be two minutes after arrival.

In the real world, all those assumptions add up.  In a blended scenario at rush hour, if a passenger picks up the HSR timetable, entries for SF Transbay and San Jose will be no less than 42 minutes apart (30.5 minutes express run time + 3.5 minutes Millbrae stop + 3 minutes Transbay + 1.5 minutes padding + 1 minute energy efficiency + 0.5 minutes slowing for San Jose + 2 minutes dwell at San Jose.)

While a special one-time midnight Cannonball Express run could be achieved in 30 minutes and 22 seconds without violating any speed limits or laws of physics, this figure is not operationally feasible in everyday service and boils down to nothing more than a stunt.  Under the same stunt assumptions, a decrepit old Caltrain diesel could rush from SF to SJ in just 39 minutes.

As the HSR project is litigated, the distinction between a one-time high-speed stunt and a robust every-day train timetable will be important to keep in mind.