18 December 2011

The Baby Bullet Effect

 For many years prior to 2004, including throughout the dot-com boom, Caltrain operated an all-stops a timetable with less stop-skipping (see February 2000 example) that fairly well revealed the underlying ridership demand at each station.  In 2004, that all changed with the advent of the Baby Bullet.  While the Bullet was a marketing triumph and remains a successful source of ridership and revenue, there was an under-reported flip-side to this new service: many small (and not-so-small) stations lost service.

Caltrain publishes annual ridership counts for each station, which can be distilled into a single table of historical counts of weekday boardings for each station reaching all the way back to 1992 (download 55kB Excel spreadsheet).  This data reveals interesting patterns.

The share of ridership at each station, which was fairly stable over several years leading up to the 2004 launch of the Baby Bullet, settled into a new pattern that has shown itself to be fairly stable in the years since 2004.  The change in each station's share is shown in the figure at right (also available as a 141kB PDF file), where 100% represents each station's average ridership share over the period 1999 - 2003, or the initial size of its slice of the ridership pie back in the pre-bullet days.  Following 2004, some slices got bigger, while other slices got smaller.  The entire pie also got a bit bigger, although that is not shown in this figure of the proportional trends for each station; ridership has only recently exceeded the 2001 peak.  The Baby Bullet Effect has divided stations into two groups: winners and losers.  Most of the losers were small and could justifiably be dispensed with.  Some were not, and are under-served to this day:
  • California Avenue in Palo Alto, 1376 weekday boardings in 2001, down to just 895 at last count
  • Lawrence in Santa Clara, 1309 weekday boardings in 2001, down to just 531 in 2011
  • Santa Clara, 1124 weekday boardings in 2001, down to just 656 in 2011
  • Burlingame, 985 weekday boardings in 2001, down to just 675 in 2011
  • Belmont, 892 weekday boardings in 2001, down to just 369 in 2011
  • San Bruno, 844 weekday boardings in 2001, down to just 403 in 2011
All of these places have more residents and jobs than implied by today's poor ridership, and are consistently under-served by Caltrain.

Planning for the Future

The future timetable plans revealed so far by Caltrain, including their notional electrification timetable and the timetables evaluated in the blended operations analysis, consist of an all-skip-stop service pattern as illustrated at left which "bakes in" the ridership pie slices as they exist today.  While the Baby Bullet is slated to be discontinued, its negative impact will live on at the places listed above, which will continue to be served by only two trains per hour (out of six).  Stakeholders at those stations should not allow this to happen.

As they plan their future operational concept, it is important that Caltrain base their stopping pattern on raw population and jobs data and not on the highly distorted ridership patterns induced by the Baby Bullet Effect.

06 December 2011

Holiday Required Reading

HSR Done Right

Sometimes, it's useful to look beyond the peninsula for context on what works best locally.  Here's a graphic from Richard Tolmach (in the latest TRAC Newsletter) that pretty much says everything that needs to be said about the California High Speed Rail Project.

As can be observed, the route that Tolmach and other organizations (including the plaintiffs in the Atherton lawsuits) have been advocating for years is very different from the route that the CHSRA is stubbornly advancing through the environmental clearance process.  In the Bay Area, the notable departure from the official plan is that HSR would branch off from the peninsula rail corridor at Redwood City, head over a new Dumbarton crossing, and zoom across Altamont Pass along the SETEC Alignment.

What does this have to do with anything peninsular?  Plenty, as it turns out.  Read on.

Caltrain's Blended Analysis

Caltrain recently published its analysis of the "blended" proposal, where Caltrain and HSR would share the peninsula rail corridor using less ambitious and expansive infrastructure than the four-track viaducts originally envisioned by the CHSRA.  This analysis concludes that it's feasible to run mixed Caltrain / HSR operations, although Caltrain service would be bunched up (with irregular skip-stop service patterns limited to six trains per hour) and HSR would need to slow down (about 40 minutes, rather than the planned 30 for SJ-SF) and be limited to 4 trains per hour.  On page 46, the document mentions that
The increased two-track shared use corridor distance from Whipple Avenue to San Jose Diridon, makes it very difficult for a 110 mph train to leave San Jose without encountering delay prior to reaching the overtake, and for a southbound HSR train to keep from being delayed by the Caltrain train it follows after the overtake.
Translation: sharing tracks should be done for the bare minimum distance, and certainly not 50 miles from SF to SJ.  Branching HSR off the corridor in Redwood City is a scenario that was NOT analyzed because it runs against Pacheco orthodoxy.  There is little doubt that it would make for an operationally superior solution (as computed by our free service pattern generator) with more Caltrain service, more Caltrain expresses, better transfer opportunities, easy-to-memorize clockface service patterns, and 125 mph HSR speeds... better in every way than the best scenarios LTK could come up with given the flawed assumptions of the study.

Speaking of better service planning...

The Swiss Take On California

Switzerland arguably has the most advanced, integrated and optimized rail service planning in the world.  The Swiss rail operations consultancy SMA+Partners supported a doctoral thesis analyzing the California rail network (including HSR) from an operations perspective.

Ulrich Leister's thesis (see executive summary) "applies a lean and rational approach to planning that is network and schedule-based.  A precise computer model is used to test different ideas such as infrastructure layouts or train types.  Gradually, the schedule is refined and optimized until the required rolling stock and the minimal amount of infrastructure needed to operate all the scheduled trains is determined."

This operations-first approach will likely come as a breath of fresh air to readers bewildered by our local experts' cost-maximizing ways.  A full copy of the thesis will be linked here as soon as it is made available.  Note in the network diagram at left that the Altamont route is identified as operationally superior, which will come as a surprise to CHSRA consultants who stubbornly insist Pacheco is the only way to go.

The Japanese Take On California

About a year ago, the East Japan Railway Company gave the CHSRA a peer review of their operations and maintenance approach.   Section of this document addresses mixed service with other rail carriers.  It is reproduced in full below, with links added to relevant articles that echo the exact same points on this blog.
Based on JR East's experience of operating conventional train and Shinkansen train on the same track, following three aspects should be carefully considered.
First, the timetable should be carefully planned. The shared operation segment is likely to be the bottleneck of the high speed train timetable since delay in the conventional line will affect the entire high speed trains network. Therefore, if transport capacity is required, 'parallel' timetable (that is, High Speed Train and conventional train operate at the same speed) or increase the capacity of the commuter trains and reduce the frequency will be the solution. To establish a more flexible timetable, additional facilities will be required both in high speed train and the conventional lines. For example, siding tracks are required in stations in this segment, commuter train vehicles with good acceleration should be implemented, speed restrictions on curves should be reduced, more signals should be allocated, etc.
Second, rolling stock should be taken account. If the High Speed Train vehicle width is different from that of conventional trains, platforms must be trimmed, and/or boarding steps must be installed either on the high speed train or on the commuter train. These boarding steps may exceed the loading gauge at some areas, so they should be stowed away while the train is running. The difference in height of the doors of the rolling stock should also be taken into consideration. Finally, compatibility of Automatic Train Control system for high speed train and conventional train should be considered. Since the safety equipment is indispensable for either train, multiple safety equipments must be installed on the rolling stock, and radio communication system must also be shared. These must be switched at the border station. Preventing malfunction both on the wayside and on-board is also important.
All this good advice has clearly fallen on deaf ears.  For example, platform interface coordination is not even remotely on Caltrain's radar, and the HSR project is actively working against it.

18 November 2011

ERTMS Coming To California

The CHSRA recently added to its collection of technical memos a White Paper on train control technology for California's high-speed rail system.  The selected train control system will likely be deployed on the peninsula rail corridor later this decade or in the early 2020's, regardless of what "solution" Caltrain may pursue in the interim.  The CHSRA's experts looked far and wide for the best technical solution, and as longtime readers of this blog may have guessed, they conclude as follows:
The sole technology that is fully compliant with all of the CHSRA project and technical requirements is the European Rail Traffic Management System (ERTMS) European Train Control System (ETCS) Level 2 with Global System for Mobile Communications – Railway (GSM-R). ERTMS is service-proven and its attributes are highly applicable to CHSTP automatic train control (...)
The biggest technical obstacle for importing ERTMS to the U.S. is the lack of available radio frequency spectrum.  The White Paper delves into great detail about possible ways to overcome this, making several important policy statements along the way:
  • The choice of train control technologies will be limited to solutions that have been successfully demonstrated at high speeds for a period of at least 5 years, to minimize implementation risk and enable a strong safety case to be made to the FRA.
  • The CHSRA requires that it not be locked into a single source for procurement, bidding, and supply. Interoperable, interchangeable, open standard and multi-vendor solutions are required and will provide the CHSRA with several sources of supply for extensions, upgrades, and maintenance spare parts in the present and future, thereby lowering risk and cost. (Are you listening, Caltrain?)
  • Other alternatives to ERTMS are not technically compliant, not compliant with the project requirements, or present too much risk to implementation.
As it happens, the coveted ERTMS / ETCS Level 2 is transparently compatible with ERTMS / ETCS Level 1, which the White Paper describes as follows:
ETCS level 1 is designed as an add-on to or as an overlay on a conventional line already equipped with wayside signals, and possibly as a fallback solution from ETCS level 2. Communication from the track to the train is ensured by dedicated balises located on the trackside adjacent to the wayside signals at required intervals, and connected to the nearby interlocking and/or wayside signals.. The balises have a data connection to the ATC equipment which provides movement authorities for transfer to the train. Receiving the movement authority through balises, the ETCS onboard equipment automatically calculates and indicates to the train engineer maximum permitted speeds of the train and the next braking points if needed, taking into account the train braking characteristics and the track description data. This information is displayed to the train engineer through a dedicated screen in the cabin. The speed of the train is continuously supervised by the ETCS onboard equipment.
This is of course precisely the same thing as CBOSS, which Caltrain and their vendor Parsons Transportation Group are now kludging together for us for a hefty wheel-reinvention fee.

We've already seen Caltrain work with FRA bureaucrats to avoid re-inventing a double-deck EMU train.  Why can't they also work with CHSRA, FRA and FCC bureaucrats to avoid re-inventing a train control system?  The CHSRA is already putting together a plan for scaling the regulatory mountain, with more detail on radio frequency spectrum acquisition provided in TM 300.03 EMT Radio Frequency (RF) Spectrum Acquisition Strategy.

It's no longer just a blogger saying it (bloggers don't know what they're talking about): the high-speed rail project is now firmly on the record as preferring ERTMS as the sole solution, and is already working with government and private entities to obtain the necessary radio spectrum to deploy GSM-R in California.  ERTMS is the best solution for the peninsula, because it would allow high-speed trains to use Caltrain tracks with no special equipment or modifications.  As a side benefit, it would also allow Caltrain to meet their PTC requirement at minimal cost and risk.

ERTMS is coming.  Your move, Caltrain.

12 November 2011

Business Plan Impressions

The CHSRA's Draft 2012 Business Plan is out.  First impressions:

Sticker Shock.  In apples-to-apples 2010 dollars, the cost has soared from $4.7 billion (2008 Business Plan) to $5.4 billion (2009 Business Plan) to a jaw-dropping $13.6 billion (2012 Business Plan).  And that's just the start.  The $13.6 billion estimate is for Option A from the Alternatives Analysis, which is the all-viaduct-and-no-tunnel option.  Community demands for trenches and tunnels will only bid up the price from there.  Toss in the San Francisco DTX tunnel and convert to YOE dollars, and the cost goes right off the charts.  Amazingly, the business plan does not actually specify how the new peninsula costs break down.  The changes in each sub-total have to be backed out from available information, as shown below from 2009 to 2012:

Until Hell Freezes Over.  Under the phased implementation plan described in the Business Plan, the peninsula rail corridor might not get improved until the late 2020's, so any hope that Caltrain had to get HSR money for capital projects, blended or not, is pretty much on hold for a long, long time.  A solid plan B will be required for Caltrain, without relying on the HSR tooth fairy.

Three Things: Concrete, Concrete, and Concrete.  The most significant cost increases, on the peninsula and statewide, are due to a breathtaking increase in the scope of concrete-pouring.  The $13.6 billion peninsula figure includes $3.9 billion for viaducts, $3.1 billion for tunnels, about $2 billion for buildings and stations, and nearly a billion for earthwork and retaining walls (the dreaded berms).  Oh, and by the way, the business plan was prepared based on cost estimates from civil engineering firms, firms that get to define the scope of the project on which they may later bid.

Atherton Real Estate is Cheap.  The feared eminent domain battles for whatever corridor expansion might be planned barely show up in the bottom line, with a mere $830 million or six percent of the peninsula budget allocated to Right of Way acquisition.

The Astronomical Cost of Accommodating Caltrain.  While the current paradigm may be that HSR would operate in the Caltrain corridor, the business plan cost numbers (and especially the must-read cost increase numbers) suggest quite the opposite, with Caltrain cast in the role of the expensive interloper.  There are surprisingly high cost numbers built into the 2012 Business Plan to build over/under/next to Caltrain even while it continues operating.  For example:
  • $2.3 billion (2010$) of additional viaduct construction expenses, "associated with staged construction, loss of efficiency, and allowance for force account and premium pay - all to account for continuous support of rail operations in the corridor."
  • $1.9 billion (2010$) for a single-track tunnel to squeeze four tracks through Millbrae between neighborhoods, planned developments, and BART, in an area where "soils are very poor"-- a tunnel that would have no reason to be built without Caltrain.  The cost of this tunnel was previously decried at $0.5 billion, but this is something else entirely: the single-track tunnel, built in the same "very poor" soils as the triple-track Millbrae BART tunnel, would cost significantly more than the entire BART to SFO extension project.
  • $0.75 billion (2010$) to build a duplicate set of tunnels along the Bayshore Cutoff into San Francisco-- multiple tunnels that would have even less reason to be built without Caltrain.
You can see the planets slowly starting to line up: in due course, somebody, somewhere is bound to point out, in the upcoming "Value Engineering" phase, that a $5+ billion premium to keep Caltrain operating is far more expensive than simply extending BART down the peninsula from Millbrae to Santa Clara to ring the Bay.

That a peninsula BART extension would be suggested as a cost-saving measure is flabbergasting indeed, but this Business Plan fairly well guarantees it.

30 October 2011

Blended Like Oil and Water

The Caltrain-HSR blended proposal, initiated by State Senator Simitian, Congresswoman Eshoo and Assemblymember Gordon to break an impending political impasse on the peninsula rail corridor, has now been evaluated by the HSR Authority's consultants.

Their version of it, submitted in a recent report to the legislature, would cost an astonishing $5.3 billion, even more than the $4.2 billion that the entire peninsula section was estimated to cost back in 2008.  This stunning price tag could have several possible explanations:
  1. a repudiation of the blended approach, accomplished by deliberately inflating the budget.
  2. an effort to pour the largest possible amount of concrete, regardless of actual operational benefit.
  3. sheer engineering incompetence and complete disregard for the new fiscal reality.
A Closer Look At Costs

While the detailed breakdown of that project budget is not provided, it's not too hard to back it out based on what is described.  Here's how it might approximately add up, including project management and contingency costs:
  • $0.3 billion to build grade separations at 25th, 28th and 31st Avenues in San Mateo, and to expand the corridor to four tracks from the southern border of San Mateo up to the vicinity of 9th Ave (milepost 18.3), with new four-track stations built at Hillsdale and Hayward Park
  • $0.3 billion to expand the existing grade separations in Belmont and San Carlos to four tracks.  This would include new stations built at San Carlos (south of the current location) and Belmont.
  • $1.0 billion to fully grade-separate the rail corridor through Redwood City, with expansion to four tracks and an elevated station.  New grade separations would be created at six locations: Whipple, Brewster, Broadway, Maple, Main, and Chestnut.  The new four-track section would tie in to the existing four-track section at Redwood Junction.  Should the Redwood City grade separations be built below grade, costs would be even higher.
  • $0.5 billion to burrow a single-track tunnel under the Millbrae station to "save" the existing Caltrain / BART station from complete demolition.  As described in the Alternatives Analysis, the station itself would be re-arranged to accommodate a segregated HSR platform at grade and the southbound Caltrain platform underground.  The tunnel approach would require two new grade separations at Center St. and Santa Paula.
  • $1.0 billion to build a six-mile (yes, six miles!) 60-foot tall elevated viaduct from Lawrence Expressway (milepost 40.9) all the way into the upper level of a massive new elevated HSR station complex in San Jose.
  • $0.2 billion to demolish existing overpass grade separations at De La Cruz (Santa Clara) and Hedding (San Jose), to be replaced with underpasses to make way for the six-mile viaduct.
  • $1.5 billion to electrify the entire corridor, an estimate based on Caltrain's latest electrification budget but discounting the cost of Caltrain's new electric train fleet.
  • $0.3 billion for positive train control and technical integration with the HSR system's train control system, which will differ from the PTC solution adopted by Caltrain.
  • $0.2 billion for reconfigured station facilities at San Francisco and San Jose.
TOTAL:  $5.3 billion

All of these individual investments must be examined in the context of their operational utility, i.e. the value they add to creating a blended Caltrain / HSR rail corridor that is as flexible and efficient as possible and best meets the service expectation of rail passengers.  And on that basis, most of the above list falls woefully short.

Let's Do Some Value Engineering
  • The six-mile (yes, six miles!) 60-foot tall viaduct to approach San Jose adds little operational value compared to cheaper alternatives such as laying additional track at grade from CP Coast (milepost 44.6) into San Jose.  The corridor is mostly 100 feet wide in this area, so the need for a viaduct--let alone a six-mile long viaduct that requires demolishing some perfectly fine grade separations that already exist--is highly questionable.  It is almost an insult to Simitian et al., who specifically requested that aerial structures be minimized.  This viaduct is the outcome of lazy engineering, the sort that avoids inter-agency coordination issues by using megatons of concrete to build over Caltrain, ACE, Amtrak, VTA, BART, UPRR, Caltrans, and everybody else.  Bottom line: with some hard negotiations and minimal takes of a few slivers of industrial property, four tracks can be built at grade all the way into Diridon Station.  Savings: - $1.1 billion
  • A four-track mid-peninsula overtake facility is the key enabler of a blended solution. However, the bulk of the cost of this mid-line overtake is a massive Redwood City grade separation project that would eliminate one of the clusters of grade crossings on the peninsula rail corridor.  Is it truly necessary to do so right away in the first phase of the blended project?  Consider these two options:
    1. The CHSRA's proposed overtake facility: 9 miles long with 5 stations (potentially including the HSR stop at Redwood City, which does not help with overtaking)
    2. A somewhat shorter overtake facility: 6.5 miles long ending at Whipple Ave (milepost 24.8) with 4 stations.
    Option 2, while only 3/4 as long, entirely avoids the need to grade-separate an expanded four-track corridor clear through downtown Redwood City.  It also delays a fight against the city's inevitable demands to burrow the rail corridor inside an astronomically expensive tunnel.  The shorter overtake might make operations slightly less flexible and robust, but at the very worst, every Caltrain could be held or slowed for just two minutes to make up for that.  Bottom line: with minor timetable adjustments, the lion's share of the cost of the mid-line overtake can be avoided.  Savings: - $1.0 billion
  • The half-billion tunnel in Millbrae is the wrong answer to the question of how to fit four Caltrain / HSR tracks through this station.  The entire Millbrae complex, including 3000-car parking garage, cost about $100 million in today's dollars.  Portions of it can be torn down and reconfigured with four tracks at grade for far less than that sum.  Bottom line: whatever the engineering constraints, you simply don't build a $500 million tunnel to "save" a $100 million station--at worst, you tear it down and start over.  Savings: - $0.4 billion
  • The need to integrate Caltrain's CBOSS train control system with the HSR train control system will drive unnecessary costs, most likely resulting in what is known as "dual fitment" of train-borne signaling equipment.  Each high-speed train, California-wide, would need to be fitted with CBOSS hardware and software, with the appropriate interfaces to allow a seamless change-over when entering or leaving exclusive HSR tracks.  This is not a trivial expense, since safety-critical signaling computers approach the cost of aircraft avionics.  Bottom line: deploy ERTMS, not CBOSS.  Savings: - $0.2 billion
TOTAL SAVINGS: $2.7 billion

The very bottom line is this: we can get 95% of the bang for 50% of the buck.  Somebody needs to inject a little bit of sanity into the planning process if a blended solution is ever going to be feasible, if for no other reason that in these times, affordability determines feasibility.  That's why the CHSRA's proposal for the blended system is a disgrace, larded as it is with operationally dubious viaducts, tunnels, bridges and underpasses; in short, a project dreamed up by civil engineers writing their own checks.

09 October 2011

Meanwhile, in Rio...

It finally happened.

Last Thursday, Caltrain's board authorized the award of the first phase of a $138,135,673 contract to Parsons Transportation Group to design, procure and install the Caltrain-specified CBOSS train control system (see staff presentation).  This Parsons contract forms the lion's share of a total project budget variously reported as $231 million to $251 million, or a whopping $5 million per route-mile.  According to a project schedule, the final acceptance of the system is planned for February of 2016 (52 months from now), but that assumed contract award at the May board meeting (5 months ago).

Viewed in the framework of the U.S. transportation industrial complex, where public agencies such as Caltrain transfer huge sums of taxpayer dollars to large private corporations that thrive on custom-engineering, re-engineering and over-engineering everything, this contract is business as usual, and Caltrain will probably end up, years late and millions over budget, with a partially functional PTC system.  That sets the stage for more years and millions spent to make it work with high-speed rail.

Meanwhile, in Rio...

Meet SuperVia, a commuter rail operator in Rio de Janeiro, Brazil.  SuperVia is one busy system, even busier than BART.  Here's a quick comparison between Caltrain and SuperVia:

Caltrain SuperVia
Route Miles

Routes 15
Trains about 25 about 160
Stations31 89

Weekday Ridership ~45,000 ~540,000

Like Caltrain, SuperVia is modernizing.  Among other improvements, SuperVia is installing a sophisticated positive train control system to enforce speed limits, prevent collisions, and reduce the headways between trains.  Unlike Caltrain, SuperVia chose to adapt their requirements to what suppliers already had on the shelf, and is procuring an ERTMS Level 1 overlay system from Bombardier Transportation through a contract worth 125 million Real, or about US $70 million.  (Note that the unknown scope of this contract makes it difficult to compare directly to CBOSS; for example, Bombardier's contract is unlikely to include the train-borne components.)  ERTMS, to remind everyone, is a train control standard that is quickly catching on worldwide, except here in the protected U.S. signaling market.

ERTMS Level 1 is exactly the sort of standardized train control system that would be transparently compatible with high-speed rail, which will most likely operate on its own dedicated high-speed trackage using ERTMS Level 2, a much more sophisticated version of the standard that does away with wayside signals.

The kicker?  Bombardier promises to put this new overlay signaling system into service on SuperVia's various lines from November 2012 to July 2013.  Here's how that stacks up against Caltrain's CBOSS:

Caltrain CBOSS SuperVia ERTMS
Contract award

October 2011May 2011
Initial service entry October 2015November 2012
Final deliveryFebruary 2016July 2013
Time from award to initial service48 months18 months

Time from award to final delivery52 months26 months

It's too late now to do anything about CBOSS, but it sure will be interesting to see what PTG and Bombardier will deliver for each respective rail system.  Can PTG and Caltrain come up with an ersatz-ERTMS by 2015 for the promised sum?

21 September 2011

Port Scores Pork

The Port of San Francisco recently received $3 million from the FRA to upgrade the 1-mile Quint Street lead track that connects the port to the peninsula rail corridor.  The government's press release states (with emphasis added) :
Port of San Francisco, California – Quint Street Yard Track and Signal Improvements – $2,970,000 to improve an approximately one mile-long spur connecting a Caltrain mainline track to the San Francisco Rail Yard. The mainline is under consideration for use as part of the California high-speed rail project, and the current condition of the spur track limits the frequency, weight and length of trains that can use the track, causing delays. The improvements will allow freight trains to operate at higher speeds and clear the mainline more quickly, significantly reducing delays to Caltrain commuter trains and future high-speed rail trains.
Meanwhile, back in the real world, Caltrain has been granted a waiver of compliance from certain FRA crashworthiness regulations that enables the operation of lightweight electric rolling stock from European manufacturers.  The same waiver would presumably be extended to any high-speed trains that might use the peninsula rail corridor.  The FRA's waiver decision letter states (with emphasis added) :
JPB additionally explains that the Caltrain 2025 program will temporally separate freight and passenger operations between San Francisco and Santa Clara, CA (Mileposts 0.2 to 44.6).  Temporal separation between these mileposts will be achieved by limiting freight movements to the exclusive freight period hours of midnight - 5 a.m.
That's right, temporal separation means that freight trains will not operate in the same hours as passenger trains, making the need to "clear the mainline more quickly, significantly reducing delays to Caltrain commuter trains and future high-speed rail trains" nothing more than a specious pretext.  Nice play for $3 million, nonetheless!

Temporal separation, by the way, is the best way to avoid the expenditure of millions upon millions of dollars to make Caltrain's positive train control system compatible with Union Pacific freight PTC (and thus, incompatible with the HSR train control system).

04 September 2011

Development Oriented Transit, Again

Protecting the peninsula rail corridor right of way from crowding or outright encroachment, whether by private developers or other agencies, has evidently not been a high priority for Caltrain.  Examples abound: a movie theater built right next to the tracks in San Mateo, a "Transit Village" planned right next to the corridor in San Carlos, a Millbrae station that constricts the number of tracks.  All of these examples complicate the task of outfitting the corridor for high-speed rail service, and may add tens to hundreds of millions of dollars to the cost of doing so.

Here we go again!

Depot Circle, a large residential/commercial development authorized by Redwood City's recently updated Downtown Precise Plan, threatens to encroach on a vital piece of station real estate in Redwood City.  The city recently released a Request for Qualifications that outlines the project and describes its role as a future focal point for Redwood City's downtown.

Here's the problem: the railroad right of way is only 60 feet wide in this area, but the station is nearly certain to be expanded to four tracks with two island platforms to accommodate the following likely operational scenarios:
  • the mid-peninsula high-speed rail stop, since neither Palo Alto nor Mountain View seem likely to welcome a station, and also because Redwood City has the best freeway access of all three corridor locations under consideration;
  • Dumbarton commuter service, long planned but unlikely to be left with sufficient track capacity to continue beyond Redwood City under a constrained "blended" Caltrain + HSR plan--thus forcing passengers to transfer at Redwood City, hopefully across a common platform;
  • a mid-line overtake location, where Caltrain express trains could exchange passengers with Caltrain local trains, across a common platform.  One of the most promising mid-line overtake scenarios now being considered under Caltrain's corridor capacity analysis assumes that four tracks would be built right through the Redwood City station.
The Depot Circle RFQ asks prospective developers to address the rail corridor issue only tangentially, without offering specific design constraints: "Describe your strategy for dealing with the potential widening of the Caltrain railroad to accommodate High Speed Rail. In particular, explain how far, if at all, would you set the project structures from the current railroad, and any other site design strategies that might be employed to minimize effects of a potential future widening of the railroad."  What are developers supposed to know about railroads?

Here are some specific constraints, which are based on detailed HSR technical requirements and Caltrain engineering standards:
  • A four-track elevated station with two island platforms will be at least 125 feet wide (if built as narrow as possible), more than 200 feet wide (if built to the CHSRA's elephantine station design standards), and over a quarter mile long.
  • A four-track underground station, however unlikely to be built because of the astronomical price tag, would need even more space to accommodate temporary shoo-fly tracks during construction (30 feet), space outboard of the trench walls for construction equipment movement (15-20 feet each side), as well as clearance for trench wall tie-backs that can't interfere with nearby building foundations.
  • Even if the station were moved north or south from its current location, away from Depot Circle, the tracks would still need to spread apart gradually (in conformance with the track alignment standards) and would occupy a wide swath well before and after the station itself.
The upshot of all this: including reasonable building setback clearances, a prospective developer should make an allowance of at least 150 feet for the future expansion of the rail corridor.  A 150-foot corridor is shown overlaid on the Depot Circle parcel map in the graphic at left (see also overlay on original map, 1.1 MB PDF), and takes a significant bite out of the parcels now offered for development--including the project's namesake traffic circle.

If Redwood City wants to become what Palo Alto could have been, it's time for the city, Caltrain, and developers to make the station itself the focus of downtown, provide it with enough land, and build it to be as architecturally striking as the elevated Amsterdam Bijlmer Arena station.  If there isn't enough vision to do that, please just avoid hemming in the rail corridor.

20 August 2011

CBOSS vs. Metrolink PTC

UPDATE 8/22 - There are a couple of additional points that require clarification.

(1) It is claimed that Caltrain's CBOSS budget is so high because it is a turn-key system provided entirely by the vendor, whereas Metrolink's PTC is being done partly in-house. But Metrolink's in-house PTC costs are included in the $202 million estimate (see page 7: $77M Metrolink, $90M vendor, $30M contingency). This does not make the comparison any more favorable to Caltrain.

(2) It is claimed that the standards for high-speed rail PTC are immature. Not so; the requirements are found in pages 723 to 825 of the HSR system requirements report (as of August 2010) as well as in HSR technical memoranda TM-3.3.1 ATC System Concept and others in the 3.3.x series. The kicker (as far as Caltrain is concerned) is that those documents clearly state that "the technology must already exist as part of an operating system with proven experience worldwide on at least one high speed passenger railway"... in other words, CBOSS need not apply, and ERTMS (now being installed by sensible commuter rail operators in places like Rio de Janeiro and Auckland) is most welcome.

ORIGINAL POST - The FRA's push to impose positive train control on all U.S. passenger railroads was triggered by the 2008 Chatsworth collision on Metrolink, in which 25 people died and 135 were injured. Not surprisingly, Metrolink's effort to meet the FRA's December 2015 deadline for PTC implementation is in the national spotlight. If a PTC success story was ever needed, it would surely have to be in Los Angeles.

Metrolink is very much like Caltrain, in that it operates diesel-powered double-decker commuter trains that occasionally intermingle with freight trains. Weekday ridership is similar at about 40,000 trips. Being in the same state, Metrolink's regulatory environment is the same as Caltrain's. One struggles to think of "unique local conditions" that might make Caltrain materially different from Metrolink.

According to Metrolink's funding plan for the project, the total budget for Metrolink's PTC system is $202 million, an amount now fully funded. Not to be outdone, Metrolink plans to complete the system a year before the federal deadline.

Here is a summary comparison table of Caltrain and Metrolink.

System Route Miles

Fleet Size (Locomotives + Cab Cars)
Weekday Ridership
PTC Total Budget
$202 million

$250 million
PTC Planned Completion
end 2014
end 2015
PTC Funding Status
$202M (100%)
<$100M (<40%)
PTC Interoperable with Freight

You might think that for the quarter-billion dollar price tag of CBOSS (Caltrain's PTC project), one would get something extra, like future-proof compatibility with high-speed rail. But alas, no. At a recent Friends of Caltrain meeting, deputy CEO Chuck Harvey confirmed that due to schedule pressure, CBOSS development would forge ahead without any regard to high-speed rail, and that HSR would have to "pay to play," with a possible requirement of "dual fitment," i.e. two separate PTC installations on-board each high-speed train in all of California. Never mind that the statewide HSR fleet would dwarf Caltrain's.

So, if HSR compatibility is not on the agenda, then what makes Caltrain any different than Metrolink? Why is CBOSS going to cost millions more than a PTC system for six times the route length and nearly twice the fleet size, to be delivered a year earlier? Why not realize economies of scale and pattern Caltrain's PTC project after Metrolink's, which has far more stakeholders in a successful outcome?

That is a quarter-billion dollar question.

13 August 2011

Corridor Capacity Study, Free Edition

You may have heard that Caltrain is working on a corridor capacity study, to see how much high-speed rail traffic could be accommodated on the corridor without adding too many passing tracks or destroying commuter service quality.

While we wait for the outcome of this study, below is a decomposition of the problem into a range of possible solutions.

Some solutions have very little downside for HSR or Caltrain service:
Other solutions require compromise between the needs of high-speed rail passengers, the needs of commuter passengers, and the needs of surrounding communities.
  • Slow down HSR, with lower top speed and all stops (Millbrae and Redwood City) made by all trains
  • Close low-traffic Caltrain stations such as Atherton and Hayward Park
  • Make peak-hour trains skip more stops-- which unfortunately denies frequent commuter service to communities precisely at the times when it is most needed
  • Build additional grade separations wherever four tracks are required
Before we make any of these painful compromises, however, the most effective measures that do not require compromising service quality should be prioritized and vigorously pursued.

If one had to bet a six-pack of one's favorite microbrew (worth several orders of magnitude less than LTK Engineering's consulting contract), the outcome of the capacity study is likely to be:
  • With 6 Caltrains per hour during the rush, spare capacity available for HSR is minimal on the existing tracks
  • Capacity can be increased most effectively by matching train average speeds, i.e. slowing down HSR and/or speeding up Caltrain
  • HSR trains will probably average no more than 60 mph between SF and SJ
  • A mid-line overtake facility between Whipple @ Redwood City and 9th Ave @ San Mateo (requiring minimal new grade separations) would improve peak corridor capacity from 6 to 8 tph
We shall soon find out if we got our money's worth.

25 June 2011

The Truth About CBOSS

$16 million was recently awarded by the FRA for the CBOSS project, Caltrain's Communications-Based Overlay Signal System. Caltrain CEO Michael Scanlon states in a Caltrain press release: "This initial federal investment will enable Caltrain to take an important step forward in our efforts to provide Bay Area communities with a modernized, sustainable commuter rail system that is fully compatible with future high-speed rail service". His counterpart at the California High-Speed Rail Authority, Roelof van Ark, intones in a CHSRA press release: "This latest step forward in federal support for California’s project means that we’ll be able to improve safety and service in the near term and integrate our project with local systems in the long term."

Fully compatible with high-speed rail service? Integrate HSR with local systems? Really?

Let's take a closer look.
As regular readers know, CBOSS has often been criticized on this blog. Rather than rehash extensive previous commentary on CBOSS, let's rely on cold, hard facts obtained solely from primary source documents. You get to decide!

The Evidence

Exhibit A: Caltrain CBOSS Request For Proposal Package, Questions Received and Answers No. 3, dated 6 October 2010. Question #20 from a prospective bidder: "What assumptions should me made in terms of HSR? (Interoperability, Operations, sharing track, etc.)" The answer from Caltrain: "Under current RFP Scope of work, HSR Operations is not considered for this phase of PTC implementation."

Exhibit B: Caltrain CBOSS Request for Proposal Package, Questions Received and Answers No. 4, dated 9 October 2010. Question #16 from a prospective bidder: "Part 2, Section 3, Exh B, Spec 21001, 1.03D requires the system to be interoperable with California HSR signaling. HSR is undefined at this stage. As this solution is not known, Contractor cannot assess any effort associated with this interoperability requirement. Please clarify how Contractor should assess." The answer from Caltrain: "Interoperability with HSR signaling is not part of the Scope of work for Caltrain PTC system RFP."

Exhibit C: Caltrain CBOSS Request for Proposal Package, Questions Received and Answers No. 6, dated 15 October 2010. Question #31 from a prospective bidder: "The RFP addresses HSR. What assumptions should the proposer make in order to address HSR requirements?" The answer from Caltrain: "Evaluation of the potential for the proposed solution to meet future HSR needs will not be part of the proposal evaluation."

Exhibit D: Caltrain's Positive Train Control Implementation Plan, a 183-page document required by law to be submitted to the FRA and detailing how Caltrain will implement its new signaling system, mentions HSR exactly once in the introduction on page 1-1. That's a slight improvement over a previous revision of the document, rejected by the FRA, which did not mention HSR at all. Section 5.1 of the document, discussing Interoperability with other railroads, does not mention or discuss HSR. Appendix D, containing letters of understanding to coordinate PTC implementation with other rail entities, does not include the CHSRA.

Exhibit E: Caltrain's Positive Train Control Notice of Product Intent, a 50-page document that describes how CBOSS will operate, explains in Appendix A section 12 the interoperability with other rail entities. Out of five paragraphs, four mention the Union Pacific, and zero mention California high-speed rail.

Exhibit F: The California High-Speed Rail Authority's extensive collection of technical memos includes Technical Memo 3.3.1, released 25 June 2010, detailing the concept of the system that will be used to control trains on the high-speed rail network. Section 1.2.4, Automatic Train Control Specification Requirements, states "The prime requirement for the CHSTP ATC system is that the technology must already exist as part of an operating system with proven experience worldwide on at least one high speed passenger railway." CBOSS clearly does not fall into this category, which means CHSRA will necessarily use another train control system than CBOSS on its own tracks.

Serious Questions

In light of all this evidence, the happy talk about CBOSS paving the way for HSR rings hollow, and raises some serious questions:
  • Is the Caltrain leadership (board and CEO) even aware of the details of the program being carried out by staff and consultants? Do they know that interoperability with HSR is explicitly excluded from the CBOSS RFP?

  • What is the plan for making CBOSS interoperable with HSR? Might it make sense to develop such a plan before awarding the CBOSS implementation contract, which may happen in the next couple of months?

  • Does the $251 million budget for CBOSS include the cost to make CBOSS interoperable with high-speed rail, as specifically excluded in the current RFP, or will taxpayers be asked for even more money?

  • Does the Caltrain and CHSRA leadership (respective CEOs and Boards) know that California HSR is slated to use a different train control system than CBOSS?

  • If California high-speed trains will use another train control system than CBOSS, why is federal HSR money being spent on the development of CBOSS? Can or should Caltrain expect HSR monies to cover the remaining 90% of the CBOSS cost that is not yet funded?

  • How, why and when were existing train control technologies, such as ERTMS, the standard that shows the strongest signs of being favored for HSR in California (see TM-3.1.1 section 6.1), eliminated from consideration on the peninsula corridor?
The local press has spent numerous column-inches, sometimes even two-page spreads, covering the Caltrain CEO's compensation package. But this is $16 million we're talking about, heading rapidly for $251 million. And not a peep from the press.

25 May 2011

The Root of the Problem, Visualized

All of the engineering design work for HSR on the peninsula is predicated on a future service plan described in Appendix K of the Alternatives Analysis, featuring 10 commuter trains per hour per direction and 8 high-speed trains per hour per direction, with no timetable coordination whatsoever. The service pattern generator can now display this for you graphically, showing where four tracks would be needed to operate this particular service pattern. We already knew the answer: four tracks everywhere along the entire length of the peninsula.

13 May 2011

Where Four Tracks Will Be Needed

"Phased Implementation" is really about asking where will four tracks actually be needed? Before this concept was floated, the basic idea was to lay four tracks all the way up the peninsula, a solution that requires little intelligent thought, but gobs of money.

The way to answer this question objectively is to play with timetables. Actually, a sequence of timetables, each of which represents a "Phase." For Phased Implementation, a "Phase" could be defined as follows:
Phase: a coherent set of capital improvements that enable a new timetable that provides better service, by some agreed-upon set of metrics, as compared to the old timetable.
We already described one example of how you might define service metrics for Caltrain, and these could be expanded to measure HSR service quality. The metrics, regardless of how they are defined, need to be timetable-independent, clear, concise, and transparent to the public. Discrete capital improvements, i.e. construction projects, can then be priced out on an individual basis and examined in the context of the new timetables that they enable. The idea is to pick the low hanging fruit first, and to build the improvements that produce the biggest improvement in the service metrics for the least construction cost or community disruption, i.e. the biggest bang for the buck.

The Service Pattern Generator

To exemplify the phased planning process and to make it more accessible to the armchair service planner, we can take the train performance calculations previously presented and fold them into an automatic service pattern generator that generates a graphical representation of a timetable and immediately highlights where additional tracks will be needed on the peninsula corridor.

Try it for yourself: Service Pattern Generator

Rather than work with tables of departure times, this tool specifies intuitive clockface timetables as graphical position-versus-time string diagrams, based on a few basic parameters for each type of train on the peninsula corridor:
  • Train type, as described in the train performance calculations, which determines how many seconds it takes a train to travel from one stop to the next;
  • Speed limit of the track, which can be considerably lower than the train's capability and also determines stop-to-stop times;
  • Station stopping pattern and dwell times, strongly influenced by whether or not level boarding is provided;
  • Frequency in trains per hour, or conversely, the clockface interval. For example, 4 trains per hour = 15 minute interval;
  • Time offset in minutes from the top of the hour. This offset determines where this train meets other trains in the service pattern, and ultimately determines where you need overtaking tracks;
  • Schedule padding, in percent of the overall end-to-end run time. 10% padding is a reasonable value.
Using these parameters, the various overlapping service patterns that describe Caltrain locals, Caltrain expresses, and high-speed trains can quickly be specified. While the service pattern generator may initially take a while to grasp, it is worth experimenting with it to develop an intuition for how a blended service plan could actually work.

The key output of the service pattern generator is the yellow highlighting that indicates where trains will catch up and overtake. In these locations, triple or quadruple tracks will be required. The challenge is to develop service patterns that provide good service for both peninsula commuters and long-distance travelers, while minimizing the cost and community disruption that comes with additional tracks.

Professionals do this using much more powerful software that can quantify how resistant these timetables are to cascading delays, but the ultimate results might not be too far off from what this simplified tool produces, when using conservative values for dwell and padding. Far from trying to do the pros' job for them, this exercise empowers the public to understand the trade-offs that must be contended with.

Working Smarter, Not Harder

Using the service pattern generator, we can explore a few examples of how to produce maximum bang for the buck.

Example 1: here's what Caltrain might look like with a mid-line overtake, often mentioned on this blog as the next logical step after (some would even say before!) electrification. Expresses meet locals at Hillsdale to exchange passengers across the same platform. Only one new grade separation is required at 25th Ave. The local holds for three minutes at Hillsdale so that downtown San Mateo can remain with two tracks. This is a typical illustration of cost vs. benefit: the hundreds of millions needed to quadruple-track San Mateo have to be weighed against the two-minute savings for the local. In this particular example, your metrics would tell you that it's not worth it.

Example 2: here's what things might look like with 3 high-speed trains per hour thrown into the mix. We now assume the entire corridor has been upgraded for 100 mph operation, which presumably implies major grade separations and crossing improvements. Introducing HSR requires quadruplication from South San Francisco (well, probably Bayshore) to Burlingame. The bottleneck at San Mateo is allowed to remain with two tracks. Further south, Atherton and Menlo Park are spared while Palo Alto and Mountain View require quadruple tracks. These two new overtake sections illustrate what would be required to provide a reasonable starting level of HSR service via Pacheco. Notice how no enormous civil works are required anywhere in the terminal areas, whether in San Francisco (no expensive tunnels starting at Bayshore) or San Jose (no hulking multi-level station). Transbay to SJ HSR trip time is less than 45 minutes; this can be reduced by increasing the HSR speed limit to 125 mph, but as you'll see if you try it, considerably more construction would be required. Are the few minutes saved worth the extra investment?

Example 3: in the never ending Altamont vs. Pacheco debate, Pacheco proponents often point out that this route is clearly best for Caltrain because it "improves" Caltrain all the way to San Jose. Try this for improvement: here's a service pattern where high-speed trains don't gum up the corridor and head for Altamont from Redwood City. This pattern assumes 4 trains per hour Caltrain local, 4 tph Caltrain express, 4 tph HSR to San Francisco, 4 tph HSR to San Jose via the East Bay, and 4 tph of Dumbarton local commuter rail. 20 trains per hour is a very high level of peninsula train service, probably more than the region will ever need... and look!
  • No expensive new SF tunnels starting at Bayshore
  • All Caltrain service terminates at Transbay
  • Two tracks through Burlingame and San Mateo
  • Two tracks through PAMPA (Palo Alto Menlo Park Atherton) and all the way south to Santa Clara
All this is enabled by only two overtake sections, grade separation of the northern half of the corridor, and punchy 6000-kW Electric Multiple Units (and also, to be fair, a new Dumbarton crossing).

Announcing: the Peninsula Blended Plan Contest

If you like the power of experimenting with service patterns, there's a contest you can enter! Entries may be made in the comments section below by copying and pasting (or better yet, linking) the URL string of your favorite service pattern, with a short paragraph to describe why you think this is the best balance of service, cost, and community impact. Entries will be judged by an impartial panel of armchair experts consisting of Clem and Richard Mlynarik (the brains behind the tool), whose own service patterns will not count for the contest.

The grand prize, a big shiny ASCII trophy known as the Takt Cup, will be awarded in two weeks.

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.