07 May 2011

Calling All Service Planners

The recent talk of phased implementation and a "blended" Caltrain + HSR system has some people proposing new service patterns and new timetables. That's a healthy thing: service planning should always drive infrastructure decisions. To ground this discussion in reality, these proposed service patterns must reflect realistic train performance that doesn't require Star Trek warp drives (or, for that matter, four tracks everywhere from San Francisco to San Jose...)

Using a Train Performance Calculator, we can find out how long any given train will take to travel from point A to point B, taking into account grades, rail adhesion, aerodynamic drag, traction and braking curves, line speed limits, etc. The results of such calculations are presented below for four key types of rolling stock on the peninsula rail corridor. With these run times, you've got all the building blocks you need to build your own strings, and from those strings, your own timetable.

The trip times can be downloaded as an Excel spreadsheet (82 kB) or a PDF document (106 kB) with eight separate tables (each in its separate worksheet) corresponding to the scenarios described below. They are reasonably accurate, but perhaps not down to the second.

Caltrain Diesel Train

The prototype for the first set of run times is a standard Caltrain consist, with one F40 locomotive and five gallery cars. The diesel locomotive is rated at 3200 hp, and the entire train weighs 420 metric tons fully loaded with 500 passengers. The train is technically capable of reaching a top speed of 100 mph, although signal system restrictions (planned to be removed) constrain it to 79 mph today.

Note: despite their bullet nose, the Baby Bullet trains have essentially the same performance.

Diesel Multiple Unit (DMU)

The prototype for the following run times is a Siemens Desiro Classic DMU. This DMU is in common use around the world, including here in the United States (although it is not compliant with FRA crash regulations). The train performance specs are based on San Diego's Sprinter, with a four-car consist as shown in the photo. Total power output is 1680 hp total for a train weighing 392,000 lb fully loaded. Top speed is 75 mph; because of this limitation, the run times are valid regardless of the track speed limit.

Electric Multiple Unit (EMU)

The next set of run times is for a Stadler KISS EMU. This six-car double-deck EMU, similar to the types under consideration for Caltrain's electrification project, has a top speed of 125 mph. The spec sheet shows that the train weighs about 325 metric tons fully loaded with 500 passengers, and is rated at 4000 kW (5300 horsepower).

The EMU's secret weapon is the ability to unleash a short-term (few minutes) burst of 6000 kW (over 8000 horsepower), which takes it into the same performance league as a high-speed train. This is handy for performing overtakes on the express tracks without disrupting high-speed traffic--a key capability for a "blended" Caltrain + HSR plan. This trick is not possible with a DMU, which is more akin to a moped entering a freeway. The run times below are for the same train using its 6000 kW short-term rating, to be used sparingly.

High-Speed Train

The final set of run times is for a state-of-the-art high-speed train of the sort that might someday be used in California. It is an 11-car Alstom AGV with a top speed of 220 mph, but used in this case at far lower speeds. The train weighs 404 metric tons and has a very high power output of 9120 kW (over 12,000 hp) as is common for high-speed trains. Generic high-speed train specifications have been compiled by the CHSRA.

If you missed the download link above, here it is again for all the above scenarios: Excel spreadsheet (82 kB) or PDF document (106 kB)

Rules of Thumb
  1. These run times are start-to-stop times only, with no intermediate stops, and do not include dwell or padding. Think of them as the fastest possible timing from Point A to Point B without stopping.

  2. Dwell time at stations is not included, and must be added separately. Caltrain dwell times can generally be assumed to be about 45 seconds if level boarding is not provided (i.e. there are steps into the train), or 30 seconds if level boarding is provided. Reduced dwell times can provide enormous savings for frequent-stop commuter trains. High-speed train dwell times should be (per TM-4.2 Phase I Service Plan) 90 seconds at intermediate peninsula stops, and 120 seconds in San Jose.

  3. Padding is not included, and must be added separately. Without padding, a timetable can only be run under perfect conditions. In the real world, stuff happens, and padding ensures that the entire timetable doesn't collapse like a row of dominoes. A good rule of thumb is 20 seconds of padding per stop.

  4. Speed limits ought to be selected carefully. It is unlikely that speed limits will increase where grade crossings are still present. (While this is technically permissible under FRA regulations, state regulations are more restrictive, based on the risk profile of each individual crossing. On the peninsula these crossings typically have a lot of road traffic.)
Building Strings for a Timetable

With the preceding rules of thumb in mind, it becomes a reasonably straightforward exercise to build a "string" that describes the position versus time of any given train, whether it be local, limited, express or long-distance HSR--based on the prevailing speed limit, train type, and stopping pattern. For example, we can construct the timetable for Caltrain 216, departing 4th & King at 7:19 AM, using the following building blocks:
  • 4th & King to San Bruno: 691 seconds
  • Station dwell at San Bruno + padding: 45 + 20 = 65 seconds
  • San Bruno to Burlingame: 314 seconds
  • Station dwell at Burlingame + padding = 65 seconds
  • Burlingame to San Mateo: 148 seconds
  • etc.
By the time you get to San Jose, it all adds up to an 8:25 AM arrival... three minutes early by Caltrain's timetable, but that has some extra generous padding at the end of the run, in order to juice their on-time statistics.

Once you've built a few "master" strings for the basic Caltrain and HSR service patterns that you envision, you can put them on a spreadsheet and slide them around to build the best-possible clockface timetable. When you do this, make sure that no two strings in the same direction of travel ever come within less than about 3 minutes of each other--otherwise, passing tracks will have to be added to allow the strings to touch or cross. This process illustrates how a timetable can tell you where the four-track sections are actually needed.

Bear in mind the limitations of this simplified approach. The most beautiful timetable can fall apart when things don't go according to plan. The pros use expensive software that can figure out how robust a particular timetable will be to the inevitable perturbations, something that factors heavily into service planning. That particular aspect of the problem isn't dealt with here.

Happy timetable building.

The Small Print

The trip times were calculated in Octave using numerical integration of the differential equations of motion. Traction, friction and drag curves are taken from train specification sheets; where not available, these are calculated based on weight on drivers and power (for traction) and the modified Davis equation (for friction and drag). Curve and terminal area speed restrictions are included. The speed limit assumptions include: 35 mph in the Transbay Transit Center; 40 mph out to 4th & King; 65 mph at Bayshore; 70 mph at Sierra Point; 75 mph at San Bruno (assumes new grade separation); 75 mph at Millbrae; 85 mph at Hayward Park; 80 mph at Palo Alto; 70 mph at Lawrence / Bowers; 45 mph in the San Jose approach. All trip times take into account the 0.6 mile discontinuity in the milepost numbering near CP Coast. All trip times assume that the train accelerates and brakes at the maximum service rate, and maintains a margin of 2 mph below the speed limit at all times. Small (few-second) differences in northbound vs. southbound trip times are ignored. Results should be accurate to about ten seconds. Your Mileage May Vary.


  1. One question about the AGV: what acceleration profile are you assuming for the train? The graph you provided on CAHSR Blog a few days ago seems to assume initial acceleration of almost 1 m/s^2, but the acceleration curves provided by the CAHSR technical memo and by Alstom suggest initial acceleration closer to 0.65 m/s^2.

  2. Two things--

    (1) I actually got the AGV traction curves on Alstom's site. Starting effort is 270 kN, versus 225 in the other document I linked.

    (2) It doesn't actually matter much. The train's acceleration profile is determined mostly by the power-limited portion of the traction curve, not the adhesion-limited low-speed regime.

  3. The table below shows a run time simulation result for the San Jose through 22nd Street route segment. A performance comparison can easily be made between Caltrain’s current 5 car trains and possible future rolling stock configurations. Local service trains call on all weekday stops contained in the present schedule. The local service has 20 intermediate stops and the express service makes 9 intermediate stops. This simulation assumes no track speed limitations except for a 65 mph San Bruno Curve and an 80 mph Sierra Point Curve speed limit. The wind resistance constant used on power limited calculations produces a resistance equal to a 0.5% grade at 87 mph. Each train has 200 passengers giving a 71% load factor except for the 5 car diesel Caltrain simulation.
    Comparing Caltrain’s current 5 car and 2 car performances by taking into account each train’s power vs. weight, wind, and, rolling impedances and each engine’s wheel to rail traction limits (0.25) shows that the total period required for train movement for the current weekday local stopping pattern declines 3 minutes 50 seconds for every car removed. Thus a schedule designed to accommodate a 5 car train can be reduced 11.5 minutes with a two passenger car consist if dwell times remain at 50 seconds. The present 50 second average dwell may be possible to sustain or even reduce if (a) two car local trains leave immediately after an express train during heavy traffic periods and (b) if wheel chair aid platforms (now available at major stations) are available at every station.

  4. Adirondacker1280007 May, 2011 23:10

    two car local trains leave immediately after an express train during heavy traffic periods...

    Heavy traffic periods by definition are when there are more passengers. Replace the 5 car local running at 71% of capacity with a 2 car local it runs at 177 % of capacity. Screws your dwell time too because instead of having 5 sets of doors to use they only have 2 sets of doors. Pesky passengers.....

  5. Clem: the starting effort according to Alstom is 270 kN, but that's for an 11-car train, which at 17 tons per axle weighs a little more than 400 tons.

    It matters a little. It works out to a difference of 15 seconds of acceleration time, which is 11 seconds of acceleration penalty when the maximum speed is 200 km/h. Not terribly important, but still...

  6. @Alon: not sure what is the discrepancy you're trying to point out. I used the Alstom spec sheet, but posted a link to an older CHSRA memo that may have muddled the issue. The numbers here are for an 11-car (200 m) train with 12 bogies, six power packs and a total mass of 404 metric tons.

    More interestingly, if they truly want to do SJ- Transbay in 30 minutes, some serious curve remediation will be needed. Or far more likely, they will have to settle for a 40 or 45-minute run, once the marginal cost of each minute saved is actually determined. While that's not "legal" under Prop 1A, money doesn't grow on trees.

    @John Bacon: what point is it that you wish to make? I couldn't quite make heads or tails of it. Level boarding is a far more productive and future-proof enhancement than somehow bending over backwards to perpetuate the anachronism of 50-second dwells.

  7. Are you sure that operating speed is really what matters most for Caltrain? That matters if your whole universe is peak commuters, but this corridor can support high-frequency, two-way, all-day service. That requires you to think about how frequency, manifested as wait time, will undermine the advantages of a fast train.

    Caring about frequency, then, means caring about staffing. A train that needs only one employee on board may be a lot more important than a train that's a little faster, because staffing will drive what frequency is possible.

  8. Are you sure that operating speed is really what matters most for Caltrain?

    Absolutely sure. To maximize the capacity (in trains per hour, stops per hour at a given station, seats per hour, or whatever capacity metric you wish to use) on a corridor that has disparate service types with disparate average speeds, you must try to match the average speeds to the maximum extent possible before even attempting to construct a timetable.

    That means the super express has to slow down a bit, and the all-stops local has to speed up a bit. Those are measures that, if not undertaken up front, will reveal themselves to be of the highest importance once you actually try to assemble a conflict-free timetable.

    That matters if your whole universe is peak commuters

    Sizing the necessary infrastructure (which is the ultimate goal of the timetable exercise) is entirely a matter of accommodating the peak. Off-peak doesn't matter, in the sense that if you can accommodate the peak, you've already solved the off-peak problem.

    staffing will drive what frequency is possible.

    Yes, but designing a timetable around union pay scales is probably not the best way to start.

  9. Adirondacker1280009 May, 2011 12:34

    Are you sure that operating speed is really what matters most for Caltrain?

    Half hour slow service - one that takes 90 minutes to get between San Francisco and San Jose means your best time is 90 minutes and your worst time is two hours. Fast hourly service between San Jose and San Francisco, one that only takes an hour means you best time is an hour and you worst time is .... the same as the worst time on the frequent service.

  10. Frequency matters, but an acceptable frequency tends to be proportional to trip time. On Caltrain, the average peak hour trip is over 20 miles, and even a half-hour frequency would be fairly acceptable. Anyway, during rush hour, frequency is driven by capacity more than convenience for commuter. One thing you have to keep in mind, though, is that Caltrain is competing against driving, and especially during off-peak periods it loses pretty badly. Who cares if you have to wait half an hour on average (for hourly service) if you're already wasting nearly an hour compared to driving?

  11. @ arcady,

    Like you said, frequencies are proportional to trip time, and low frequencies will stymie desirability for short trips. I think it's unfair to use the logic that Caltrain should only cater to longer trips because that's the rider profile of today. Perhaps people only take longer trips because there's a lack of frequent local service and there's limited compact development around the stations. With many TOD developments planned at many of the stations along the line, I think it's important that frequent, all-day local service is provided in addition to the peak express service.

  12. Of course we'd like Caltrain to be all things to all people, but we have limited space and money, and for reasons that Clem explained fairly well, this means we have a tradeoff between line capacity and the number of different average train speeds. This leads to an inevitable tradeoff between local and express service, and means we need to set priorities. And I would argue that it's best to make Caltrain prioritize regional travel, by which I mean trips of 10 to 40 miles, as opposed to local or long distance travel. For long distance travel, it's not too much of a compromise to make them slow down a bit to fit in with Caltrain's timetable, and the number of long-distance travelers is always going to be small compared to commuters. For local service, there are alternatives in the form of the local light rail and bus, including "rapid" bus systems. They might not be quite as good, but they're there. For "regional" travel, there really isn't much of an alternative other than driving. But if Caltrain makes "regional" travel the priority, it still needs to serve the local stops, because nothing says that 10-mile trips all begin and end at the same places, which are 10 miles apart. So there will still have to be service to the local stations, it just might be less frequent than is desirable for local travel. Then again, given the existing alternatives (VTA and SamTrans), a 30 minute headway is really not too bad for local service. Ideally, 20 or 15 minutes would be even better, but that's also partly a matter of whether the demand is there to run that sort of service economically.

    I'd also like to point out that Caltrain lost little if any ridership when they reduced midday service from 2 to 1 trains per hour, despite the fact that the trains make all local stops and are thus better for use as local transit than the rush hour trains.

  13. Clem, is the DMU a fair example? According to this page, there are DMUs capable of ~90 mph top speeds, which have a better weight-to-power ratio that those used by the Sprinter:


    "Currently delivered Itino units reach their top speed of 87 mph in 112 seconds"

    I would think that we should compare fast DMUs to EMUs, if we want to prove that electrification is the real need. Based on my understanding of modern DMUs, I believe that getting an FRA waiver and buying good DMUs could provide 50% of the benefits of electrification, at least until HSR needs to share the tracks. Or are high power-to-weight ratio DMUs not possible?

  14. Clem wrote "Iif they truly want to do SJ- Transbay in 30 minutes, some serious curve remediation will be needed. Or far more likely, they will have to settle for a 40 or 45-minute run"

    Why? Your 125 mph HSR table shows <34 minutes from San Jose to 4th/King, with current curves and the extra stops. Running express from SF to SJ should save about 1.5 minutes per stop eliminated, or 7.5 minutes total, which seems like enough to get from SJ to Transbay in 30 minutes flat.

    Or am I missing something?

  15. Joseph, Clem's table is for nonstop trains. The HSR table includes nonstop times for all pairs of express stations, but it should not be confused for a schedule of trains making all express stops.

  16. Adirondacker1280014 May, 2011 21:51

    If a train makes all the stops it's not an express.

  17. All express stops. Sigh. To put it in terms you'd understand: if the MTA publishes nonstop travel time for station pairs on the 2 between Chambers and 96th, it doesn't mean that a train making all 2 stops can achieve the same travel time.

  18. I think my selection of trains is fair. While there are faster and slower DMUs, the Desiro is a much more widely used model worldwide than the Itino. The Itino has been a disaster for operators, with brakes failing and engines and transmissions needing replacement, so I'd hardly use that as an example.

  19. Adirondacker1280015 May, 2011 09:55

    Having the 6 stop at 96th street doesn't make it express. But during rush hour there are express 6 trains. The not stopping at all the stations part is what makes it an express. If it stops at all the stations in the Bronx it's a local.
    The mighty HSR train leaves Los Angeles and doesn't make any stops until San Jose then all the HSR stops until San Francisco it's a Peninsula Local. The mighty HSR train leave Los Angeles making all stops until San Jose and then not stopping until it gets to San Francisco it's a Peninsula Express. They are going to have to come up with a name for the peak trains that leave Los Angeles and don't stop until they get to San Francisco.

  20. Adirondacker12800,

    That naming can be relatively easy with a hint of how many stops there will be.

    100's ->

    101, 102, 103, etc. are for trains with one stop in between SF and LA

    200's ->

    201, 202, 203, etc are trains with two stops in between SF and LA


    800's ->

    801, 802, 803, etc are trains with eight stops in between SF and LA

    Or, you could get tricky by giving every station a number, ie. SF=1, San Jose=2, Fresno=3 and LA=4. Then, train 1341 stops at SF, Fresno and LA and being the first one of the day with that routing (1342 would be the second with the same routing). 10041 would be the first SF-LA direct. You can get really creative with numbers, but people might not understand them.