Primarily Two Tracks

Figure 4 from Caltrain's study, showing several possible locations for new overtake tracks.  Not all would be built.

In recent days, the high-speed rail Draft Revised 2012 Business Plan as well as the Caltrain Blended Operations Analysis were released to the public.  Both of these documents refer to the peninsula blended solution as a "primarily two-track" system, in the hope of allaying fears of massive eminent domain takings of homes and business-- fears that are largely unfounded, but fanned relentlessly by the local press and project opponents.

The confusion continues over what "primarily two tracks" precisely means, because neither agency seems ready to come out yet and state it in crystal clear terms.  The process still needs to unfold.  Luckily, enough data has already been published to allow a reasonably good reading of the tea leaves, down to the nearest tenth of a mile.

Phase 1 will be electrification, according to the memorandum of understanding currently being put in place by MTC and other parties.  This project already has federal environmental clearance and is very close to state environmental clearance, although a strong push will be made by opponents to subsume Caltrain's electrification EIR into the peninsula HSR project EIR, a document that will not be finalized (let alone litigated!) until 2015.  This phase of the project will not add any tracks, so the total length of quadruple track will stay as it is today (2 miles in Brisbane; 1 mile in Redwood City; 2 miles in Sunnyvale).

• Purpose: improves Caltrain, enables future peninsula HSR
• Time frame: 2013 - 2019
• Total miles of quadruple track: 5
• Grade-separated fraction: 61% (64 of 104 road crossings)
• Trains per peak hour per direction: 6
• Cities impacted by construction: none

Phase 2 will be a concrete viaduct through Santa Clara, completed at the same time as HSR reaches San Jose sometime in the mid-2020's, enabling a one-seat ride to San Francisco under the so-called "Bay-to-Basin" scenario.  If the CHSRA's grandiose plans (described in an October 2011 report to the legislature) are to be believed, this will entail building a massive double-decker station complex at San Jose.  A new four-track HSR station will hulk over the existing Diridon Station, perched on massive concrete straddle bents.  A more than 3-mile-long, 60-foot-tall viaduct will be constructed northwards, joining the existing corridor at approximately milepost 44.5, north of the Santa Clara Caltrain station.  Overpasses at Hedding and De La Cruz will be demolished and rebuilt as underpasses to make room for the new double-deck rail right of way.  Note that Caltrain's study considers this phase as part of the "baseline infrastructure" and therefore does not count it as additional tracks.

• Purpose: enable single-seat HSR ride to San Francisco
• Time frame: mid 2020's
• Total miles of quadruple track: 8
• Grade-separated fraction: 61% (64 of 104 road crossings) 
  
• Trains per peak hour per direction: 8 (6 Caltrain + 2 HSR)
• Cities impacted by construction: Santa Clara

Phase 3 will be the "short" mid-line overtake from 9th Ave in San Mateo (milepost 18.3) to Whipple Ave in Redwood City (milepost 24.8), which enables HSR service to increase from 2 to 4 trains per hour during the peak.  The data tables in Caltrain's study show that this overtake facility provides nearly all the benefits of the "full" mid-line overtake that extends southwards through Redwood City, but presumably at far lower cost.  The transportation-industrial complex's approach to the short mid-line overtake might very well entail demolishing the entire Belmont - San Carlos grade separation and replacing it with a four-track viaduct on concrete stilts.  A more realistic implementation will likely be to tack on another 15 feet of width on each side of the existing grade separations to accommodate new overtake tracks, something that should have been done in 1999 (but why do it right when you can do it twice?).  In San Mateo, new four-track grade separations will be built at 25th, 28th and 31st Avenues.

• Purpose: increases HSR peak capacity from 2 to 4 trains per hour per direction
• Time frame: late 2020's
• Total miles of quadruple track: 14.5
• Grade-separated fraction: 63% (67 of 106 road crossings) 
  
• Trains per peak hour per direction: 10 (6 Caltrain + 4 HSR)
• Cities impacted by construction: San Mateo, Belmont, San Carlos

Phase 4 will be the "full" mid-line overtake, also known as the Great Redwood City Grade Separation, creating a new mid-peninsula HSR stop at Redwood City and grade-separating a dense cluster of six grade crossings.  The four-track mid-line overtake will be extended southwards to milepost 26.3, merging with the existing four-track section.

• Purpose: adds mid-peninsula HSR stop
• Time frame: late 2020's
• Total miles of quadruple track: 16
• Grade-separated fraction: 69% (73 of 106 road crossings) 
  
• Trains per peak hour per direction: 10 (6 Caltrain + 4 HSR)
• Cities impacted by construction: Redwood City 

Beyond that, it gets murkier.  Presumably, the 33 remaining grade crossings that are not removed under Phases 1 - 4 will be addressed on a case-by-case basis, with grade separations designed and built in consultation with the respective cities.  San Francisco's downtown extension to the Transbay Transit Center may finally be built.  Additional passing tracks may be constructed where it's relatively easy and cheap, for example the remaining 2.5 miles from Lawrence to Santa Clara and the "north overtake" in Caltrain's study, an additional 8.2 miles of quadruple track from Brisbane south into Burlingame.

Only one thing is quite certain: the peninsula rail corridor will categorically NOT remain a two-track operation, even if it might still use "primarily" two tracks.  At a minimum, approximately 16 miles or over a third of its length will be quadruple-tracked.  As the process unfolds, it will become apparent that the cities of Belmont, Redwood City, San Carlos, San Mateo and Santa Clara will be the first to suffer the construction impacts.

The Hybrid DMU, Unicorn of the Rails

The hybrid DMU is a diesel multiple-unit train with a twist: it has on-board energy storage to enable energy recovery, similar to an electric train that feeds power back into the grid when slowing down.  Just as in a hybrid automobile, this energy store helps to start the train rolling again, and reduces energy consumption in stop-and-go operations.  Peninsula cities and stakeholders, ever more astute on rail matters, perceive three important benefits in the hybrid DMU:

1. It keeps high-speed rail out.  In discussions of Caltrain electrification and the slow beating-around-the-bush process that is leading up to the certification of the electrification EIR, high-speed rail has become the central issue. Electrification is viewed in some quarters as the camel's nose under the tent, so a renewed push is underway to ensure that all the alternatives other than electrification have been duly considered.
    
2. It keeps unsightly high-voltage poles and wiring at bay, preserving views and presumably residential property values in some of the most affluent areas in the nation.
    
3. It spares Caltrain, the perennially funding-starved agency, the burden of spending $785 million of scarce capital dollars to string wires over its tracks.

The hybrid DMU is viewed as a synergistic technology that solves all three issues in one fell swoop, in a classic Silicon Valley win-win-win.

There's only one little problem: it doesn't really exist.

Okay, almost.  There do exist a handful of hybrid DMUs in Japan.  These advanced technology trains, instantly knowable to any city staffer via a simple Google search (keyword hint: 'hybrid DMU'), operate in Japan.  The fleet numbers three cars on one line, and ten cars spread among four other lines.  Each car seats about 45 and tops out at 60 mph.  Their power output is less than a Chevy Tahoe hybrid's.

The Law of Diesel Trains

To understand why the hybrid DMU will never work for the peninsula corridor, look no further than the laws of physics.  What Caltrain needs is a singular focus on better service: quicker trips, more frequent stops, higher capacity, and less waiting for the next train.  That requires big, fast trains with one key quality: punchy acceleration, precisely the reason why the EMU (electric multiple unit) powered by high-voltage overhead lines was invented and perfected.  To achieve high acceleration, the laws of physics dictate high power and low weight.

A diesel train makes all its power on board and sends it to electric motors that drive the wheels; it is essentially a rolling mini power plant.  The nicest and newest rolling mini power plants used by Caltrain today generate 3,600 horsepower for a million-pound train.  In metric units, that's about 6 kW/ton, and as any Caltrain rider can attest, it doesn't exactly pin you to your seat.  The problem is that rolling mini power plants are heavy, and if you want more power, you'll need to haul around even more weight.  This is the Law of Diesel Trains, directly derived from Newton's Laws of Motion.  More weight does little to help with acceleration, so diesel basically can't scale up.

The EMU, on the other hand, doesn't schlep around a rolling mini power plant.  Its electricity is generated off-board by a real power plant, of the PG&E variety.  The electric grid, hooked up to gigawatts of generating capacity, can provide essentially limitless power to a train.  That endows a typical EMU (of the sort available off-the-shelf from many manufacturers) with a power-to-weight ratio of about 12 kW/ton, or double the giddy-up of a diesel train.  For short bursts of acceleration, high-voltage EMUs can briefly exceed their continuous power rating and draw even more power, hitting up to 18 kW/ton.  For those still keeping track, that's triple the acceleration of Caltrain.  For reference, BART cars achieve a respectable 15 kW/ton.

So what do the Japanese know about hybrid DMUs that we don't?  Most importantly, they do not claim zippy acceleration as a benefit.  The hybrid DMU does three things for them: save about 10% on fuel, cut down nitrous oxide emissions, and cut the noise of an idling train down to an electric whisper. Beyond those benefits, the 'D' in DMU makes it follow the Law of Diesel Trains.  The Japanese hybrid DMUs manage barely 5 kW/ton, probably because they haul around not just a mini power plant, but also big heavy batteries.  Here in the US, more stringent crashworthiness standards would make such trains even heavier and their performance even more anemic.

The inescapable conclusions are thus:

• Hybrid DMUs provide only about one third of the acceleration required to enable meaningful Caltrain service improvements. A simple technical litmus test for future Caltrain rolling stock is the power-to-weight ratio, required to be at least 12 to 15 kW/ton.  Hybrid DMUs don't qualify.
• Hybrid DMU technology has never been scaled up beyond the size of a bus.
• Hybrid DMU technology inherently cannot be scaled up to achieve higher power-to-weight and acceleration in large (600 - 1000 passenger) configurations.

The mystical powers ascribed to hybrid DMUs by peninsula stakeholders rightfully earns them the nickname of 'Unicorn of the Rails.'  It's time for them to realize that by undermining the choice of EMU technology and promoting hybrid DMUs, they are also undermining the future of Caltrain--intentionally or not.  Caltrain can be faulted for many things, but their choice of high-voltage EMU technology as the path to modernization is unequivocally correct and technically justified, regardless of what happens with high-speed rail.

Will BART Bust a Move?

The unfortunate reality of Bay Area transit politics is that twenty-eight agencies compete for funding and ridership with very limited coordination.   At the top of this pile is BART, the biggest of them all.  Not so much BART the transit operator, but BART the expansion-thirsty transit-industrial complex (functioning somewhat like the military-industrial complex), as facilitated by the Metropolitan Transportation Commission (MTC).  (photo at right by cplbasilisk, modified with permission)

With recent developments in the peninsula high-speed rail story, it's worth taking a step back and imagining BART / MTC's next moves in this slow-motion game of political chess, assuming for a moment the following motivations:

• Expand as much as possible, constructing the most new infrastructure in the most corridors using the most consultant engineering and "craft hours" of construction labor
• Soak up as much federal, state and local funding as possible
• Take over high-ridership corridors, even at the expense of other agencies
• Ring the San Francisco Bay with BART, as initially planned in the 1950s

The resulting exercise can either be viewed as a crackpot conspiracy theory, or as a simple thought experiment rooted in recent history.  Where MTC and BART have successfully assembled billions of dollars for the Millbrae/SFO and San Jose/Santa Clara extensions, Caltrain has repeatedly floundered: no downtown extension, no electrification, no Dumbarton rail, and the list goes on and on...  Supposing this historical pattern were to be sustained, what specifically would be BART's logical next moves?

Move #1: Drop Support For Pacheco HSR.

The long-running Pacheco-Altamont controversy over the Bay Area HSR alignment, still simmering in the courts, is driven on one hand by not-in-my-backyard sentiment in communities impacted by the Pacheco alignment (notably Palo Alto, Menlo Park, and Atherton) and on the other hand by transit activists who argue that the Altamont alignment makes far more technical sense to serve the immediate transportation needs of the Bay Area in a coordinated and sustainable way.

BART and MTC were firmly in the Pacheco camp because of the need to preserve for BART a key piece of rail right of way between Fremont and San Jose (the former Western Pacific line, purchased by VTA in 2002).  This right of way would almost certainly have been claimed by HSR under any reasonable Altamont scenario.  Worse, a blended HSR/commuter rail project could have undermined the very purpose and need for BART in that corridor.

Today, this concern has been overcome by events, and the BART extension to San Jose is a done deal.  Pacheco HSR no longer plays a role in defending this important BART turf, and thus may no longer garner the same level of support from BART and MTC as it once did.



Move #2: Promote Altamont HSR with a BART Connection at Livermore.

The BART board recently approved a more detailed study of a future extension to Livermore, along I-580.  While this extension is a waste of money on its own merits (as are most BART extensions), and is still far from becoming reality, it could be sold as a key enabler for a phased implementation of HSR, especially under a budget-constrained environment.

Livermore as a BART-HSR transfer point has been considered before, if only discreetly, as part of the half-hearted "Altamont overlay" that the CHSRA has been studying in addition to the baseline Pacheco Pass alignment--always with the insistent disclaimer that the Altamont corridor serves a completely different "purpose and need" than the high-speed rail project.  Meanwhile, MTC suggested as recently as 2007 that HSR terminate at Livermore BART, absorbing all HSR ridership into BART (see comment L017-8).

As an interim phasing opportunity, Livermore BART would actually work quite well:

• Earlier and quicker HSR service to downtown San Francisco and the greater Bay Area
• Earlier and quicker HSR service to Sacramento (quicker than the Amtrak Capitols)
• Cheaper construction with less tunneling to achieve "Bay-to-Basin" connectivity

The Livermore BART extension would be routed south along Vasco Rd. or Greenville Rd., past the Laboratory, to terminate just south of Livermore at a new BART/HSR interchange station on the outskirts of town.  This station would be located on an Altamont HSR alignment proposed by outside groups but studiously ignored by the CHSRA.  This Altamont HSR route is known as the SETEC alignment, after the French HSR consulting firm that performed the preliminary engineering.  The SETEC alignment is noteworthy in that it avoids major residential property impacts to Livermore and Pleasanton, one of the main arguments used by the CHSRA to select Pacheco in the environmental study process.

Here is a rough point-by-point comparison of Altamont/Livermore and Pacheco/Gilroy interim scenarios:

	Altamont HSR to Livermore	Pacheco HSR to Gilroy
HSR Trip Time, from Fresno	0:48 Fresno - Livermore	0:39 Fresno - Gilroy
Continuing Trip to San Francisco	0:57 on BART Livermore to Embarcadero	1:45 on Caltrain Gilroy to SF (electrified)
Fresno - San Francisco CBD	~ 2:00 (40 minutes quicker) including transfers	~ 2:40 including transfers
Fresno - Oakland	~ 1:50 (50 minutes quicker)	~ 2:40
Fresno - San Jose	~ 1:50 (10 minutes slower) assumes BART to SJ	~ 1:40
HSR Track Length	140 miles (25 miles more)	115 miles
Phase 2 HSR to Reach Sacramento	60 miles (50 miles less)	110 miles
HSR Tunnel Length (interim)	about 4 miles (6 miles less)	about 10 miles

Using the money saved by tunneling only 4 miles to Livermore instead of 10 miles to Gilroy, the additional 25 miles of track to reach Livermore are easily paid for-- and then some, since 50 miles of track will already have been built to reach Sacramento, as opposed to zero for Pacheco.

Move #3: Dangle the Carrot of a PAMPA Subway.

The Palo Alto Weekly recently published an article headlined "Four-track design back on the table for high-speed rail," apparently implying that it was once off the table.  That seems to be the crux of a major disconnect between the city and the high-speed rail Authority.  The blended Caltrain / HSR plan, as proposed in recent months by Simitian-Eshoo-Gordon and currently being analyzed by Caltrain, was always viewed by the CHSRA as an intermediate phase, a stepping stone to the immutable objective of a four-track high-speed railroad through PAMPA (Palo Alto - Menlo Park - Atherton).  This viewpoint is borne out in the 2012 draft business plan.  Palo Alto, on the other hand, views the blended plan as a final state of the peninsula rail corridor for the foreseeable future, and believes that the four-track plan should no longer even appear in the program EIR.

BART's best move here is again to promote Altamont HSR.  For PAMPA, the advantages are thus:

• No four-track HSR grade separations, ever
• No additional right of way (a.k.a. eminent domain) needed, ever
• No HSR traffic on top of commuter rail traffic (only 6 trains per hour per direction)
• Future opportunity for a two-track BART subway, considerably cheaper to construct than a four-track high-speed corridor.  A two-track BART tunnel box is four to five times smaller, in cross-sectional area, than a four-track HSR tunnel box.  This makes it remotely feasible to have the cities participate in the financing of a subway, much as was done in Berkeley in the 1960s, to further enhance property values.

For BART itself, the main advantage of Altamont is of course to preserve the future possibility of ringing the bay by connecting Santa Clara BART to Millbrae BART.  The argument that BART can make in pleading this case is that all existing infrastructure north of Millbrae (i.e. fresh grade separations in San Bruno, and existing tunnels to San Francisco) would be dedicated exclusively to HSR, thus mitigating the astronomical cost of accommodating Caltrain detailed in the 2012 business plan.

As billions of dollars slowly coalesce for a possible blended HSR / Caltrain plan on the peninsula, time will become pressing for BART to bust a move.  If the motives that underlie the above narrative are remotely true, then any attempt to electrify the peninsula corridor shall be thwarted, just the same as it has been in past decades.

The Bookend Approach

There's a lot of turmoil surrounding the California High-Speed Rail Authority these days.  Some want to forget the whole thing, while most sensible politicians (as well as the peer review group) seem to want to re-plan the project to start with the ends rather than the middle, so as to end up with something useful sooner--not to mention spending the federal money already allocated.  What if this actually happened in the coming months?

The first thing you can be sure of is that a tug of war would occur between the SF Bay Area and the LA Basin, with maybe just a sprinkle of money to placate the Central Valley.  Out of the six billion of federal and state monies currently available, let's assume that $2.65 billion ends up here.  Let's further assume that the money is actually spent in ways that enable high-speed rail, rather than poured down the usual black hole of BART extensions, never to be heard from again.  What could and should be built in the San Francisco Bay Area for $2.65 billion of high-speed rail funding?

The bookend approach, in order of priority:

NUMBER ONE: Deploy ERTMS, the train control system that will be used for HSR.  The peninsula corridor, which happens to be in need of a federally-mandated positive train control system but has nowhere near enough money to pay for it, could serve as the perfect testbed to import this key enabling technology of HSR to the United States.  In exchange for full HSR funding, Caltrain would agree to abandon their unfunded and HSR-incompatible CBOSS project.

• HSR benefit: pilot deployment of ERTMS standard in the US, ready for expansion to the state-wide HSR network.  All regulatory hurdles cleared.
• HSR funding share: $150 million (Caltrain can pay for other items such as the backup control facility) 
• Environmental Clearance: not required 
• Timeline: easily completed before 2015, following the example of Rio de Janeiro or Auckland.
• Independent Utility: fulfills federal PTC mandate for Caltrain

NUMBER TWO: Electrify the peninsula rail corridor, exactly as already planned.  25kV overhead lines are 100% compatible with HSR and will enable a one-seat ride to San Francisco as soon as HSR reaches the peninsula.  Out of the $1.2 billion budget for the electrification project, $400 million is for a new fleet of Caltrain electric trains, and $800 million is to string up the wires.  It would seem fair to use HSR money for 50% of the fixed infrastructure, and let Caltrain / MTC come up with other funding sources to pay for the trains and the other half of the shared infrastructure.

• HSR benefit: one-seat access to San Francisco and SFO, without changing trains in San Jose
  
• HSR funding share: $400 million (50% of infrastructure cost)
• Environmental Clearance: Complete and shovel-ready. Federal clearance is in hand, and state clearance is a simple matter of Caltrain certifying their EIR.  Preliminary engineering well underway.
• Timeline: completed by 2016.
• Independent Utility: provides faster, better, quieter, less polluting peninsula commute for over 10 million riders a year, and helps "ring the bay" with electric rail transit, relieving highway 101 congestion

NUMBER THREE: Build a mid-line overtake facility.  This 6.5 mile section of four-track railroad would expand the rail corridor from 9th Avenue through southern San Mateo, Belmont and San Carlos, ending at Whipple in Redwood City, by adding a new pair of tracks outboard of the existing tracks.  This adds just 15 feet on each side of existing grade separations.  The overtake would include new grade separations at 25th, 28th and 31st Avenues in San Mateo, and new stations with central island platforms at San Carlos, Hillsdale and Hayward Park.  Belmont already has a suitable island platform.  The mid-line overtake has already been identified as an important enabler of blended operations, by providing an opportunity for faster trains to pass slower trains.

• HSR benefit: 20 minute shorter travel time to San Francisco
• HSR funding share: $600 million (100% of the cost)
• Environmental Clearance: not started.
• Timeline: probably not complete by 2017 spending deadline of federal HSR funding, unless environmental clearance is fast-tracked.
• Independent Utility: provides reliable overtaking of Caltrain locals by Caltrain expresses, at a four-platform Hillsdale station where passengers may conveniently transfer between a local and an express that dwell simultaneously on either side of the same island platform (see diagram above).  This improves service frequencies and trip times for millions of riders a year.

NUMBER FOUR: Build the downtown extension (DTX).  This 1.2-mile tunnel would extend the peninsula rail corridor to the Transbay Transit Center in the heart of San Francisco's business district.  This is a very pricey project at $3 billion YOE dollars, and one additional complication is that MTC recently gave it a very low benefit/cost ratio--most likely to protect BART ridership on the Millbrae line, and future plans to ring the bay with BART.  (A very frank, adult conversation will soon have to be had regarding unspoken aspirations for BART to ring the bay.)

•  HSR benefit: Direct access to the jobs-rich San Francisco central business district, with excellent transit connections to the East Bay to maximize the HSR ridership catchment area on the first day of service.  Realizes full benefit of $400 million investment of HSR funds already made in the Transbay Center train box.
• HSR funding share: $1.5 billion (50% of the cost)
• Environmental Clearance: Complete and shovel-ready.  Both EIS and EIR are cleared, and preliminary engineering is well underway.
• Timeline: could be completed by 2017 spending deadline of federal HSR funding.
• Independent Utility: provides commuter access to San Francisco's central business district, where there are more jobs than near all the other Caltrain stations combined.  This would most likely result in a system ridership gain of 25% or more, easily 3 million new riders a year.

Some high-speed rail supporters will doubtless see this as a wish list of projects that benefit Caltrain at the expense of true high-speed rail.  However, these are exactly the four projects you would start with in order to build a modern standard-gauge electric railroad into the heart of San Francisco, just what is needed so HSR can run directly to San Francisco's business district from day one.  Insofar as Caltrain happens to also aspire to become a modern, standard-gauge electric railroad, yes, Caltrain benefits greatly.  But let us not forget that the non-HSR funding share to complete these four projects would be well over $2 billion; this is not a shameless and wasteful diversion of HSR funding, but a cost-effective investment in a compatible system that is more than the sum of its parts.

The very high level of "independent utility" for peninsula commuters should not detract from the fact that each of these four projects is a direct enabler of HSR service to San Francisco, effective as soon as the backbone of the system is completed using later tranches of funding.  In the meantime, the earliest investment would pay off immediately, in a way that it never could if a raceway to nowhere were built in the Central Valley.

Peninsula Rail Corridor Census

The U.S. Census Bureau provides an astonishing array of fine-grained statistics on population and jobs along the peninsula rail corridor.  When thinking about the future of peninsula rail service, and especially in deciding quantitatively how good a proposed timetable might be, or where stations should be placed, or how HSR should mesh with Caltrain in a 'blended' scenario, the basic consideration should be where people live and work.

Annual ridership counts provide one way of planning your timetable: simply add more service to the stops that get a lot of ridership.  This becomes a self-fulfilling prophecy with ridership patterns becoming distorted by the timetable, as observed with the Baby Bullet Effect.  Teasing apart the timetable-induced distortion from the underlying (and often untapped) ridership demand is impossible, so it is necessary to go back to the raw population and jobs data to build the full picture.  That is where the census really delivers.

Where People Live

Figure 1

The 2010 census provides the most recent snapshot of the population distribution on the peninsula, on a block-by-block basis that includes over 45,000 locations in the three Caltrain counties.  By tallying up how many people live within 1/4, 1/2, 1 and 2 miles of each Caltrain station location, you can build Figure 1.  This chart reveals where the population is densely concentrated around stations (e.g. San Mateo), or sprawled out (e.g. Sunnyvale).

Observations on the population numbers:

• The new Oakdale station long proposed by San Francisco (with little support from Caltrain) could tap into more residential population than just about any other stop along the peninsula, or even 22nd Street.
• The population density doesn't suddenly drop off at the southern end of the Caltrain-owned right of way in San Jose, where service suddenly drops off.  There are large concentrations of under-served population within a mile of the Tamien and Capitol stops, accounting for more than 3 times as many people as live within a mile of the San Jose Diridon station.
• A stop like Broadway (Burlingame) with zero weekday rail service has more people living near it than Millbrae, site of the all-important BART intermodal station.  Other stations with poor Caltrain service (San Antonio, Cal Ave, San Bruno, Burlingame, Belmont, Santa Clara) have more people living nearby than stops with the best service, such as Palo Alto.

Figure 2

To assign to each station location a single weighting factor that quantifies that station's accessibility for nearby residents, regardless of distance, one can sum up each person divided by the square of how far away they live.  This inverse-square relationship is empirical, but captures the fact that people who live far away from a station are less likely to use it; its use in ridership modeling is not unprecedented.  A 1/r law would fall off too slowly, with the same number of people using the station from 1/2 mile away as 2 miles away (assuming constant population density).  A 1/r cubed law would fall off too quickly, with only 1/16th as many riders from 2 miles away as from 1/2 mile away.  As it turns out, the precise value of the exponent--if not exactly two--doesn't really drive the relative weights that strongly.  Only one small tweak has been applied to prevent people who live very close to a station from skewing the results: anyone living closer than 1/4 mile is considered 1/4 mile away.  The resulting inverse-square population weights for each station location are shown in Figure 2.

Where People Work

Figure 3

The Census Bureau publishes extensive statistics on local employment dynamics, providing block-by-block data on the number and distribution of jobs, pay levels, and industries.  The latest data set as of this writing is from 2009 (based on geographical data from the 2000 census covering over 32,000 locations in the three Caltrain counties).  The analysis presented here is based on raw data files, but the data can also be analyzed interactively using the Census Bureau's On The Map application.   Figure 3 shows how many jobs are located within 1/4, 1/2, 1 and 2 miles of each Caltrain station location.  Only the jobs worth more than $40k a year are shown, since lower-income jobs are less likely to require commuting (only about 15% of Caltrain riders earn less than $40k, and the average household income of a weekday peak Caltrain rider is over $100k).

Observations on the jobs numbers:

• Not so surprisingly, there is a concentration of jobs in the vicinity of the future Transbay Transit Center, adjacent to the financial district.  What is more surprising is just how massive that concentration is: Transbay has more jobs within a half-mile radius (over 100,000) than all the other Caltrain stations combined, from 4th & King all the way down to Gilroy!
• Job sprawl shows up in Santa Clara and southern Palo Alto (and most of Silicon Valley, really) in the form of few jobs near stations but many jobs within a mile or two.  Mountain View, despite its status as a major Baby Bullet stop, and home of Google, is not a particularly large job center.

Figure 4

Again, assigning to each station a weighting factor that quantifies that station's accessibility to nearby jobs, we apply the same inverse square relationship to obtain the job weights for each station location shown in Figure 4.  Note that Transbay goes way off the chart.

The Ridership Potential Matrix

Since 86% of riders during the weekday peak are commuters, the distribution of population and jobs can be used to construct a relative weight for the ridership that could potentially be generated between any given origin and destination (O&D) pair.  This is the ridership potential matrix.  The eventual purpose of this matrix is to help derive a single figure of merit for timetables, on an apples-to-apples basis, for how much of the potential ridership is tapped based on the service metrics for each O&D pair.  When considering any given timetable, this weighting scheme ensures that O&D pairs that have a lot of population and jobs at each end (such as 4th & King and Palo Alto) are given more importance compared to O&D pairs with lower population and fewer jobs (such as Atherton and Bayshore).

It is important to note that this ridership potential matrix is completely independent of how each O&D pair is connected by rail service; it holds true for any timetable.  It is solely a product of census data and the geographic location of each station.  A timetable must then be designed to unlock the maximum potential ridership.

The ridership potential matrix works like this: take for example station 1 and station 2, with respective population and job weights P1, P2, J1 and J2.  The weight for morning peak trips from origin 1 to destination 2 is P1*J2 (for people living near station 1 and working near station 2).  Conversely, the weight for morning peak trips from origin 2 to destination 1 is P2*J1 (for people living near station 2 and working near station 1).  When you multiply all the population weights from Figure 2 by all the job weights from Figure 4, you get a basic ridership potential matrix.  But there's a bit more to it than just people and jobs.

Distance Considerations

Regardless of where people live and work, there are upper and lower limits to how far they will typically commute by rail.  Extremely short trips are less likely because of the overhead of access and egress to and from the station, at each end of the journey.  Conversely, extremely long trips are less likely because of their sheer duration; regional commute patterns are not just a factor of train service considered in isolation, but also driving times.  That's why we will make the assumption that the distance distribution of commutes, generally speaking, is independent of the quality of train service--and that no foreseeable rail service pattern could significantly alter it.  Good service might lead to greater market share for rail, but the underlying distance distribution will be assumed not to budge.  This allows us to apply a (timetable-independent) distance distribution to the ridership potential matrix.

Figure 5

Caltrain ridership surveys show that the average trip length on the peninsula rail corridor during the weekday peak is about 25 miles.  The distance weighting function will be modeled as a Rayleigh distribution with a value of 0 at 0 miles and a peak of 1 at 25 miles-- for no particular statistical reason other than it ends up looking about right, as shown in Figure 5.

Each element of the ridership potential matrix is now the product of three factors: the distance weight based on the distance between origin and destination; the population weight at the origin station; and the job weight at the destination station.  This simple formulation yields the morning peak values shown in Figure 6 as a bubble graph (numerical values are available as a tab-delimited text file).  The evening peak is described by the transpose of the matrix, i.e. origin and destination switch places.  The distance-weighted ridership potential matrix is now ready for use in the quantitative analysis of past, present and future timetables, a topic that will be covered in upcoming posts revisiting the topic of service metrics.

Figure 6

Figure 8

Figure 7

In the meantime, we can explore other interesting aspects of the ridership potential matrix.  For example, summing the nth row together with the nth column of the matrix allows us to build a single weighting factor for the potential ridership at each stop including both the morning and evening peaks, i.e. a measure of the ridership distribution that could exist if it were tapped with excellent service, shown in Figure 7.  These weights can then be compared to the actual Caltrain ridership realized in 2011, yielding the scatter plot in Figure 8.  This comparison provides another more fundamental way (much better than historical ridership patterns) to visualize which groupings of Caltrain stops are under-served, and is amazingly accurate considering that it was constructed without ever looking at a timetable.

Key conclusions:

• Access to Transbay would provide a step-change improvement in Caltrain service, with probable ridership gains of more than 25%.  Terminating any weekday peak train at 4th & King, as is inexplicably planned by Caltrain, is a huge mistake.  Agency turf battles with BART and the CHSRA regarding whether or how to pay for the downtown extension tunnel, and how to share platforms at Transbay, must be fought and won.
• Underlying ridership demand is not accurately reflected by realized ridership, which suffers from severe timetable distortion.  Future service planning, and in particular the timetables assumed for the ongoing 'blended' operations analysis, must be based less on realized ridership and more on fresh census data--even if not using the simplified approach described here.
• For the same reason that every Caltrain should serve Transbay (the huge concentration of jobs in San Francisco), HSR service that does not provide a one-seat ride into Transbay is a non-starter.