17 February 2013

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.


  1. Clem:

    Thanks for your excellent analysis.

    Using your example that present diesel hardware would make SF to San Jose under the best of conditions, in 39 minutes and comparing that to the present baby bullet actual real life trip times of 1 hours (only to 4th and King BTW, it takes 53.8% longer to do a practical route.

    Using Vacca's claim of 2 hr 40 minutes for SF to LA and applying this 53.8% factor, the trip would be 246 minutes which is 4 hour and 6 minutes. Now that is being realistic.

    1. That's a bad assumption and you know it. The rest of the CAHSR line has constrains that the Authority has failed to factor in (probably slowdowns through CV cities, etc), but they're nowhere near as serious as the issues on the CalTrain corridor. A more realistic projection of express travel time is probably about 3:00-3:10, though I lack the tools to verify this.

    2. I would caution against such cavalier math. An accurate assessment of the SF - LA trip time requires plan and profile data for the selected alignment. This should be possible to construct from Google Earth data and other published information, but it is a time-consuming process to get all the curve and profile data into the right formats. Once the data is in hand, however, it is quite straight forward to perform the simulations.

      I suppose it wouldn't hurt to check their math and assumptions on I-5, Altamont, Grapevine, etc...

    3. 3:15 isn't as good as 2:40 but it's still faster than flying or driving. Very few people are going to decide to drive from LA to SF because the train ride is 3:15 instead of 2:45.

    4. 4h00m isn't as good as 3:15 or 2:40 but is still faster than driving.

      And trains are still better than kitten killing atom bombs.

      And CHSR costs less than the Vietnam War.

      So ignore the promises, ignore the timings, ignore the budget, ignore the ridership, ignore the alternatives, ignore the unexamined assumptions --- just keep funding.

      It's the only rational choice.

  2. The LA County supervisor is already on record that he wants trains to slow to 110 mph in that area. Not sure what that does to the travel times, but I'm sure it has an impact.


    Also, as Clem has posted previously, blowing through downtowns at 220 mph is something that can't be mitigated from a noise perspective. During eventual "normal" operations, my bet is they'd slow down....

    All of which is to say, they aren't likely to be under 3 hours. Which means according to their own ridership estimates, they'll have a hard time attracting a lot of riders.

    So when will someone at HSRA realize that in order to build something competitive, they need to prioritize picking up passengers and a fast travel time? Something has to give. Altamont? I-5?, etc. Every decision has impacts on time and people...

    1. He also wants HSR to use Metrolink tracks, which is already explicitly forbidden in an agreement with UP (north of LA).

    2. It's interesting that they want a limit not based on noise - which is what they are trying to mitigate - but speed. These are of course directly related, but the goal should be 'no more than 80db at 50ft distance', then let them build it, and set the speed limit such that the noise is within that limit.

    3. It's completely normal in the US to think purely in terms of speed limits. Some people look at me with virtual horror when I suggest that some of the old bridges on the NEC can be kept for longer and with higher speed limits if the trains are lighter. It's as if speed limits are a God-given imposition.

  3. Note that running at 125 mph max speed SF-SJ as in the SF-LA runs decreases SF-SJ time from 30:22 to 29:55. What's the point of running at 125 mph if it only saves 27 seconds?

    1. The 29:55 figure assumes a slightly different set of speed limits, so it's not a direct apples-to-apples comparison to 30:22. The difference is closer to 90 seconds. But your rhetorical point stands: it's not worth upgrading from 110 mph to 125 mph.

    2. Assuming the track is straight enough and train capable of the speed, what is the cost of increasing speed from 110mph to 125mph? Is that a software upgrade to the signal system, or is there more to it?

    3. It's mostly a grade crossing and station platform safety thing. Running trains past crowded and unprotected platforms at 125 mph, while possible, is not something that we should encourage. 79 mph is scary enough, and 110 mph is already pushing it.

  4. The SF-San Jose speed graph at the top of the article says 4th St to San Jose is 47.84 miles-- you're aware at present the distance is probably 1.1 miles less than that?

    1. Well spotted, but probably irrelevant.

      The same graph shows "Santa Clara CT" (probably Santa Clara Caltrain, with the new platform at ~44.25 miles from 4th & King buffer stops) at 233085 feet or 44.14 miles, pretty much spot on. I don't know why the distance between SC and SJ might be off by more than a mile, but keep in mind their chainage can be discontinuous... see the SF - LA graphs for far more obvious examples. The speed graphs as given don't show where these discontinuities lie or how large they are.

      So, I didn't use the distance annotations at all. Instead, I went by the curve notches, which are clearly identifiable geographical points with a characteristic spacing. If you measure them accurately and calibrate to the corresponding mileposts, the proportional spacing shows that zero is definitely at 4th & King.

    2. Re discontinuous chainage:

      Caltrain Milepost (Miles! in 2013!) 44.0 just north of Santa Clara station is equated to MP 44.6: ie N to S tenths of miles count "... 43.7 43.8 43.9 44.6 44.7 44.8 ..."
      That's the only discontinuity. I don't know the reason for it, but it dates from Southern Pacific days.

      So the milepost "distance" (which itself is a convention, not a physical measurement of track length) between 4th&Townsend (MP 0.2) and San Jose Cahill Street (MP 47.5) is 47.5 - 0.2 - 0.6 = 46.7 miles, or the equivalent in furlongs and cubits.

      Santa Clara is MP 44.8, making it 44.0 milepost-miles from SF 4th&T, or 232320 spurious-precision milepost-feet.

    3. Far as we know in 1950 there were no discontinuities between SF and Lick-- zero was at end of track 3rd St SF. The Sierra Pt line change added 0.04 mile circa 1956, the move to 4th St subtracted maybe 0.16, CEMOF added 0.02, and think it was UP that remileposted the whole Coast Line to be a continuation of the Elmhurst-Santa Clara-via-Mulford line. The latter led to the suspiciously-exact 0.6-mile change near Santa Clara.

    4. Which doesn't get us any closer to an answer, since both Tim and I had already correctly taken into account the 0.6 mile discontinuity that Richard described.

  5. I thought Milepost 0 was originally One Market Street, the old SP hq.

    1. 65 Market St was built after the earthquake-- before that, SP HQ was 4th and Townsend? Suspect no one can find a timetable showing Milepost 0 for the Coast Line at 65 Market. (What would be the point?)

    2. What would be the point?

      The increase of human knowledge and welfare, of course.

      Finding and publishing this information would have as much point as any other fact-based contribution (by Clem or any of the numerous informed commenters) has had on Caltrain and HSR.

  6. The timetables for the Caltrain service get very irregular. In order to make room for the HSR service, Caltrain service effectively gets interrupted. A quick examination of the graphs can show you that to fit in an HSR run (with the steeper slops on the graphs), there's typically about a 20 minute interval between Caltrain runs. This means that the so-termed 6 trains per hour Caltrain service has service delays no better than what you'd get for 3 trains per hour. A twenty-minute wait for the next train is a huge addition to the mean travel time. If you presume that a typical Caltrain user goes half the distance - meaning 20 minute travel time, degrading the wait time from 10 minutes worst case/5 minute average to 20 minutes worst case/10 minutes average - you've degraded the service by 5 minute average/10 minutes worst case.

    To summarize, this wonky schedule degrades a typical service time from 25 minutes to 30 minutes average and from 30 minutes to 40 minutes worst case.

    So these typical half-system runs get 20% worse on average and 33% worse at worst case.

    The killer problem here, is that this degradation in worst case travel time makes Caltrain service inferior to automobile service - I know I can drive the half-system distance faster than this worst case travel time, why should I ever take Caltrain?

    1. Your criticism is applicable to any hypothetical timetable Caltrain has ever generated. They measure quality of a timetable in minutes of delay (a train-centric metric that measures only the reliability of service, and not its intrinsic quality) and does not account for wait times or service intervals other than through broad "x trains per hour" service levels for each stop. I am not hopeful that anybody can teach that old dog any new tricks.

    2. Amateur Hour with LTK.

      So very very bad.

      Teh stupid, it hurts.


      Caltrain / California HSR Blended Operations Analysis
      Supplemental Analysis Requested by Stakeholders
      Service Plan / Operations Considerations Study
      Prepared for: Peninsula Corridor Joint Powers Board (JPB) Prepared by: CalMod Program Team April 2013

      Garbage in, tenfold garbage out.

      ("CalMod". That's Hip, daddy-o.)

    3. The assumptions are still terrible, yeah, but at least they're considering not entirely eliminating CalTrain express service now.

      They show 4 tracks in Millbrae - is this still with the $2 billion tunnel?

    4. I'm looking at page 17 of the document about the Long Middle 4 Track Overtake. Unless I'm misreading this, it looks like added tracks at Millbrae are labeled "Tracks to be added (for Caltrain)". Unless the tunnels are meant to be built for Caltrain, it appears that the tunnel is off the table, at least for this analysis.

    5. I also looked at this document and Caltrain recognizes importance of memorable 30 min frequency.
      Why Caltrain don't implement 30 min frequency in the peak period? Current time table designed 2004~2005 when Caltrain has only 30000~35000 of daily ridership.If 60 min cycle is timetable for 30K ridership, we need 30 min cycle for 50+K ridership.
      I would like to see more trains instead of longer train.

  7. I don't understand why Milbrae need major reconstruction.
    Current south bound platform have space for addtional track in the east side. Addtional northbound track can be converted from BART trucks. If they need separate between Caltrain and HSR, it can be same as current Caltrain-BART separation in the north bound tracks. Currently, 2 of 3 BART track are almost no utilization.

    1. That would be applying logic to the problem, as was discussed here previously.

      Politics and institutional dysfunction dictate otherwise, and the chances of BART relinquishing even a small part of its facility are fairly remote. Only the prospect of spending 5x to 10x the cost of the existing Millbrae facility (all in order to avoid destroying it!) would perhaps move the respective agencies to some sort of agreement.