The Top 10 Worst Curves

The peninsula corridor was laid out in the mid 19th and early 20th centuries, for train speeds of that period. It is the oldest passenger line west of the Mississippi. Needless to say, rail technology has progressed enormously in the last 100 years. The California High Speed Rail Authority is now planning to run trains on the peninsula at a top speed of about 125 mph. Sounds great, but what about all the curves? (Bayshore curve photo by Michael Patrick)

Minimum Curve Radius

To allow HSR operation at 125 mph, just how wide does a curve need to be? This is an elementary calculation of railway engineering, and is determined by safety and passenger comfort. Without going into details, speed can be increased in a curve by banking the track into the turn, like a turning airplane or a freeway exit ramp. The outside rail can be canted or super-elevated a maximum of 7 inches (178 mm) higher than the inside rail. Trains can go even a bit faster than the speed that balances this banking, causing passengers to feel a sideways push to the outside of the curve. The technical term for this is cant deficiency, and under current FRA regulations it is limited to 3 inches. Within those limits (7 inches cant + 3 inches cant deficiency), physics dictates the following curve radii:

Speed	Minimum Radius	(Recommended Radius)
160 km/h (100 mph)	1200 m (4000 ft)	1800 m (5900 ft)
200 km/h (125 mph)	1900 m (6300 ft)	2800 m (9200 ft)
215 km/h (135 mph)	2200 m (7300 ft)	3200 m (10500 ft)

The recommended radius is preferred, in the absence of trackside constraints such as houses and roads, to keep passengers comfortable and reduce wear and tear on the trains and the track. Wherever curve clearances are constrained (i.e. pretty much anywhere on the peninsula), the minimum radius becomes the quantity of interest.

The Cost of Slowing Down

Slowing down from 125 mph to take a curve, and accelerating back up to 125 mph costs several seconds of travel time, compared to an uninterrupted run at 125 mph. It's just a few seconds, but if every curve eats a few seconds out of the schedule, pretty soon HSR starts losing its "high speed." So exactly how many seconds are too many? Maybe the answer lies in the cost of a second. If you assume:

• HSR annual ridership will be 60M passengers / year (considerably less than the CHSRA's estimate)
• About one third of all HSR passenger trips will include the peninsula segment
  
• The average passenger (leisure and business) values their time at $12/hour (an approximate value based on time value studies)
  
• The cost of straightening a curve is amortized over 15 years of operation (the continuing benefit beyond 15 years is free)
  

Then each second of delay costs about $1 million of lost time to HSR passengers, and could be worth about $1 million in construction costs to remediate. That does not include the ancillary benefit to Caltrain Baby Bullet passengers. One can take issue with the exact assumptions and accounting methods, but the point of this exercise is to gain a very rough order of magnitude understanding for the cost of a second: on the order of a $1 million.

Using a typical deceleration / acceleration rate of 0.5 m/s^2, the cost of temporarily slowing down for a typical curve from a cruise speed of 125 mph goes as the square of the speed difference:

Curve Speed (mph)	Time Penalty (s)	Delay Cost
115	3	$3M
105	7	$7M
95	13	$13M
85	21	$21M
75	31	$31M
65	43	$43M

The square relationship means that it's not necessary to straighten curves all the way up to 125 mph. Arbitrarily setting our threshold of diminishing returns at 5 seconds of penalty, 110 mph curves can be considered "good enough" unless they can be straightened to 125 mph within the existing right of way, essentially for free. The reconstruction of any curve below 110 mph should be weighed against the dollar cost of time lost.

While this author is not versed in the fine art of estimating construction costs, we now have enough information to at least prioritize the worst curves where something should be done, short of deciding which ones are actually cost-effective to rebuild.

Existing Curves on the Peninsula

All major sub-125 mph curves in the Caltrain corridor from San Francisco to San Jose are shown in the chart below. Milepost is plotted along the bottom, and the curve's maximum speed is plotted on the vertical axis. The maximum speed is derived from the curve radius by assuming the aforementioned 10 inches of equivalent cant, except for reverse curves where different constraints apply. (Note, these speeds are not possible today; the maximum cant on Caltrain is 5 inches to accommodate freight trains, and the signaling system allows only 79 mph.)

Click for Larger View. First, there are quite a few curves that interfere with a 125 mph speed limit, as indicated by the blue dotted line.

• Several curves fall above the 110 mph "good enough" threshold, indicated by the green dotted line, although they should still be candidates for realignment if they are easy to fix. Recall these speeds are absolute maximum speeds, with 3 inches of cant deficiency (passenger discomfort).
  
• Some curves are very tight, but would be impossibly expensive to straighten; an example is the Sierra Point curve, which runs around the base of San Bruno mountain. There are other sharp curves in the San Francisco and San Jose terminal areas that fall into this category.
  
• One curve will be avoided entirely by HSR: the infamous CEMOF double reverse curve in San Jose, where the most expensive way to avoid a curve is planned, namely a tunnel.

Leaving aside these "impossible" curves and the "good enough" curves, we can examine the remaining curves and construct a list of the worst curves for HSR on the peninsula.

The Top Ten Worst Curves

Here's a Google map, although it is much more accurate and instructive to view the KML file directly in Google Earth.


View Larger Map

#10 (Honorable Mention) CEMOF Double Reverse Curve - Milepost 46.5 - While the CHSRA plans a tunnel under this area, you really have to wonder what Caltrain was thinking when they dropped this turd on the approach to San Jose. That's why it gets an honorable mention.

#9 Belmont - San Carlos Reverse Curve - Milepost 22.4 - While we're adding another two tracks here, the incremental cost of straightening this curve to 125 mph ought to be near zero, since it can probably be done within the existing ROW. Savings: 10 seconds.

#8 San Antonio Curve (see curve detail map) - Milepost 34.3 - Great potential for straightening to 125 mph, again within the existing ROW. Savings: a couple of seconds, but it's free!

#7 Bowers Curve (see curve detail map) - Milepost 41.9 - Already OK for nearly 110 mph, but could use as much flattening as practical because of the proximity of Lawrence curve.

#6 Lawrence Curve (see curve detail map) - Milepost 40.6 - This shallow 100 mph curve can easily be straightened all the way up to 125 mph by purchasing a narrow strip of office parking lot (which Sunnyvale has plans to redevelop anyway). This is low-hanging fruit, well worth the 10 second savings.

#5 Hayward Park Curve (see curve detail map) - Milepost 18.8 - This curve was already straightened in the year 2000 by moving the rails by 20 ft. It might now support 95 mph. Would be better at 110 mph, saving about 10 seconds.

#4 Millbrae Curve (see curve detail map) - Milepost 13.9 - An unfortunate consequence of the last Quentin Kopp extravaganza, the BART airport extension. Challenge: BART tail tracks occupy the inside of this 90 mph curve. BART would have to give up one of three tail tracks to straighten for 100 - 110 mph operation. This ought to be feasible: two of the tail tracks were built in anticipation of a BART extension south of Millbrae, which no longer makes sense. Savings: about 15 seconds.

#3 Palo Alto Station - Milepost 30.1 - Already discussed in Focus on Palo Alto. While the existing curve radii are gentle, the problem at Palo Alto is a double reverse curve, which requires long spiral easements to reverse the curvature and prevents the speeds you might deduce from the radius alone. The southbound track is good for just under 90 mph. Challenge: reconfigure the Alma St. overpass; on the plus side, JPB already owns all the required land. Savings: about 25 seconds. A must-do, regardless of whether Palo Alto becomes an HSR station.

#2 Bayshore Curve (see curve detail map) - Milepost 5.1 - Just north of the Bayshore station at the mouth of Tunnel #4, this curve is a piece of cake to straighten to 125 mph, provided Bayshore station is redone. This will probably happen anyway to make room for the approaches to the planned new tunnel bores on each side of the existing tunnel. The new tunnel bores could even have curved ends. Savings: about 20 seconds. Cost of new platforms: $10M tops. Low hanging fruit, just waiting to be picked!

#1 Worst Curve: San Bruno Curve (see curve detail map) - Milepost 10.9 - previously discussed in the San Bruno article. This curve, currently 65 mph, should be straightened to 110 mph minimum. Savings: a whopping 40 seconds. Challenges: well-advanced plans by Caltrain for a new station, locking in the existing curvature; eminent domain for ~$5M worth of houses on the inside of the curve; six I-380 viaduct pillars would need to be moved. If this curve can be fixed even for $30-40M, JUST DO IT!

The total time saved from straightening these 10 curves is about 2 minutes, not including the savings from straightening the other 110 mph+ curves not listed here. These time savings add up to ~7% of the non-stop travel time between San Francisco and San Jose, expected to be around 30 minutes.

The CHSRA and its engineering contractors should not resign themselves to the existing curvature of the peninsula corridor. A rigorous study of curve remediation should be undertaken before the new track alignments are finalized.

Update - 02 Feb 09

It was brought to my attention that the CHSRA published in its considerable (if un-navigable) body of work a series of run simulations. This is what the pros do, instead of the back-of-the-envelope calculations detailed here. A sample San Jose to San Francisco run is detailed below. The train used in the simulation is a Siemens ICE 3. It does not stop in San Jose in this particular example. Total time from San Jose (running start) to San Francisco is a few seconds short of 30 minutes (1793 seconds, to be precise)

This simulation reveals a couple of interesting assumptions on the part of the CHSRA's analysts:

• Total cant is 12 inches (vs. 10 inches assumed in the calculations above) allowing 10% higher curve speeds. This is not outlandish: 12 inches is practiced today on the NEC.
  
• The Palo Alto and Bayshore curves are evidently straightened out, with a curved platform at Palo Alto
  
• None of the other bad curves appear to be straightened, as revealed by the three deep notches in the speed profile at Hayward Park, Millbrae and San Bruno.
• The train's throttle is used heavily, and the regenerative brake will certainly get a good workout. Whether this lead-footed driving style is realistic is open to discussion.
  

While these assumptions are self-consistent and do not violate any laws of physics, they are somewhat optimistic. This is another reason to straighten San Bruno curve: then you could do SF to SJ in 30 minutes with margin.

Judging a Train By Its Nose

One of the recurring themes emerging from public comments about HSR on the peninsula, at scoping meetings or on community bulletin boards, is the notion that HSR on the peninsula merely duplicates existing Caltrain service at astronomical expense and disruption to communities. The reasoning goes like this: why bother with HSR running at "half speed" on the peninsula if passengers can just catch a Baby Bullet in San Jose that whisks them into San Francisco? We've already got a bullet, so why do we need another one? If HSR is only running at "half speed" why not use the existing tracks? Those are good questions.

One thing is certain, Caltrain has scored a marketing home run with their Baby Bullet brand, borrowing the aura of high speed rail and pointy-nosed aesthetics to convey an image of speed and efficiency. Unfortunately, there are a couple of problems with confusing the Baby and its namesake.

Myth #1: Speed

"We already have a bullet. We don't need another one!"

Baby Bullets look sleek, and they impress when they blast by, horn blaring. However, they are nowhere near as fast on average as the proposed high speed trains. Timings from San Jose to San Francisco:

• Caltrain local: 96 minutes - max speed 79 mph - average speed 29 mph
  
• Caltrain Baby Bullet: 57 minutes - max speed 79 mph - average speed 49 mph
  
• HSR: 30 minutes - max speed 125 mph (a.k.a "half speed") - average speed 94 mph
  

HSR at "half speed" is still nearly twice as fast as the Baby Bullet. Suppose HSR were terminated in San Jose, and that passengers transferred to Caltrain. Accounting for transfer time in San Jose, the effective speed of the Baby Bullet ride would approach three times slower than a single-seat HSR peninsula ride. The overall trip from LA to SF would increase from 2:38 to 3:15, an increase of about one quarter. If we compromise that much on the peninsula, why even bother with 220 mph in the central valley? Indeed why bother with high speed rail at all?

Ridership is very sensitive to total trip times and changing trains. Every second counts. That is the reason for terminating HSR in San Francisco, which has a large catchment area of potential riders.

Myth #2: Track capacity

"If HSR is running at half speed, let them just use the existing two tracks!"

Mixing trains with different average speeds on the same track reduces track capacity, measured in units of trains per hour (tph). A slow train must be given plenty of time to clear the tracks ahead of a fast train that follows; otherwise, the fast train will catch up to the slow train and get stuck behind it. While modern signaling systems allow 15 tph when speeds are homogeneous, today Caltrain can only manage 5 tph at rush hour because Baby Bullets and locals operate at very different speeds. Add HSR to the mix, and what little track capacity we have would collapse.

More tracks are needed along much of the peninsula to allow trains with vastly different speeds to overtake each other, thus freeing track capacity. This ultimately has benefits for local Caltrain service as well: with Baby Bullets allowed to operate on the new HSR tracks, local track capacity will increase, enabling more rush hour service to under-served stops like California Ave or Belmont or South San Francisco.

Never judge a book by its cover. Likewise, never judge a train by its pointy nose.

Who is HNTB ?

HNTB Corporation is a large civil engineering firm that has a key role in the overhaul of the peninsula corridor. HNTB designs bridges, highways, airports, railways, stadiums, and basically any complex infrastructure that eventually involves pouring fair amounts of concrete. They have about 2700 employees in 60 offices nationwide, including a key office in Oakland and a satellite office in San Jose.

HNTB was the principal designer of the BART extension to SFO and Millbrae; they were the brains behind all the track, tunnels, aerial structures, and the South San Francisco and San Bruno stations. The actual construction was done by other firms teamed with HNTB. The BART project was politically spearheaded by Quentin Kopp, who is today the chairman of the California High Speed Rail Authority. On election night 2008, just as Measure 1A returns were being tallied, Kopp was sipping martinis with HNTB management and other firms involved in the high speed rail project. Peter Gertler, HNTB's national transit director (in charge of all things rail) and his staff are even reported to have canvassed for passage of the bond measure.

HNTB is no stranger to Caltrain: they designed the CEMOF maintenance facility in San Jose, which features an elegant reverse curve that is sure to cause yet another interesting engineering headache for high speed rail.

HNTB is now engineering the peninsula section of the HSR project, under a contract awarded by the California High Speed Rail Authority in November 2008. They will design all aspects of HSR on the peninsula, starting with basic track alignments. Their latest status report can be found here. Once the preliminary design is completed to the "30 percent" level in mid-2012, the CHSRA will put the detailed design and construction of the peninsula corridor out for bid. HNTB is certain to team with construction firms to bid on the next phase, but it is not guaranteed to win.

Here are some key names that you may see popping up, and who were in attendance at the scoping meetings. An organization chart is also shown at right, from the January status update.

• Dominic Spaethling - SF-SJ Regional Manager - CHSRA and Parsons Brinckerhoff - Sacramento

• Tim Cobb - Project Manager - HNTB West region public transit director - Oakland

• John Litzinger - Engineering & Alternatives Analysis - HNTB - San Jose

HNTB is teaming with other firms for this design work, including DMJM, Transmetrics, Prointec (a Spanish firm with 20 years of HSR experience), among others. It's nice to see some European involvement to make sure the peninsula is done right.

Caltrain Right Of Way Maps

The table below contains maps of the Caltrain right of way, with key dimensions like ROW widths and the approximate boundaries of property owned by the Peninsula Corridor Joint Powers Board (Caltrain), the Union Pacific Railroad, local transit agencies, and others. This information will be useful in discussing the impact of HSR on peninsula communities.

The maps date mostly from March 2007. This public information was provided by Caltrain upon request; thanks to Brian Fitzpatrick (Manager Real Estate & Development) as well as Martha Martinez (PCJPB Secretary). The files are provided as-is; I decided against consolidating a large PDF to spare server bandwidth and allow linking to individual areas of concern along the line.

Milepost	City	Station	PDF Map
0 to 1	San Francisco	4th & King	00-TCCM-200-B.pdf
1 to 2	San Francisco	22nd Street	01-TCCM-200-B.pdf
2 to 3	San Francisco		02-TCCM-200-B.pdf
3 to 4	San Francisco		03-TCCM-200-B.pdf
4 to 5	San Francisco		04-TCCM-200-B.pdf
5 to 6	San Francisco / Brisbane	Bayshore	05-TCCM-200-B.pdf
6 to 7	Brisbane		06-TCCM-200-B.pdf
7 to 8	Brisbane / South San Francisco		07-TCCM-200-B.pdf
8 to 9	South San Francisco		08-TCCM-200-B.pdf
9 to 10	South San Francisco	South San Francisco	09-TCCM-200-B.pdf
10 to 11	South San Francisco / San Bruno		10-TCCM-200-B.pdf
11 to 12	San Bruno	San Bruno	11-TCCM-200-B.pdf
12 to 13	San Bruno / Millbrae		12-TCCM-200-B.pdf
13 to 14	Millbrae / Burlingame	Millbrae	13-TCCM-200-B.pdf
14 to 15	Burlingame		14-TCCM-200-B.pdf
15 to 16	Burlingame	Broadway	15-TCCM-200-B.pdf
16 to 17	Burlingame / San Mateo	Burlingame	16-TCCM-200-B.pdf
17 to 18	San Mateo	San Mateo	17-TCCM-200-B.pdf
18 to 19	San Mateo		18-TCCM-200-B.pdf
19 to 20	San Mateo	Hayward Park	19-TCCM-200-B.pdf
20 to 21	San Mateo	Hillsdale	20-TCCM-200-B.pdf
21 to 22	San Mateo / Belmont	Belmont	21-TCCM-200-B.pdf
22 to 23	Belmont / San Carlos		22-TCCM-200-B.pdf
23 to 24	San Carlos	San Carlos	23-TCCM-200-B.pdf
24 to 25	San Carlos / Redwood City		24-TCCM-200-B.pdf
25 to 26	Redwood City	Redwood City	25-TCCM-200-B.pdf
26 to 27	Redwood City / Unincorporated		26-TCCM-200-B.pdf
27 to 28	Unincorporated / Atherton	Atherton	27-TCCM-200-B.pdf
28 to 29	Atherton / Menlo Park	Menlo Park	28-TCCM-200-B.pdf
29 to 30	Menlo Park / Palo Alto		29-TCCM-200-B.pdf
30 to 31	Palo Alto	Palo Alto	30-TCCM-200-B.pdf
31 to 32	Palo Alto	California Ave.	31-TCCM-200-B.pdf
32 to 33	Palo Alto		32-TCCM-200-B.pdf
33 to 34	Palo Alto / Mountain View		33-TCCM-200-B.pdf
34 to 35	Mountain View	San Antonio	34-TCCM-200-B.pdf
35 to 36	Mountain View		35-TCCM-200-B.pdf
36 to 37	Mountain View	Mountain View	36-TCCM-200-B.pdf
37 to 38	Mountain View / Sunnyvale		37-TCCM-200-B.pdf
38 to 39	Sunnyvale	Sunnyvale	38-TCCM-200-B.pdf
39 to 40	Sunnyvale		39-TCCM-200-B.pdf
40 to 41	Sunnyvale	Lawrence	40-TCCM-200-B.pdf
41 to 42	Sunnyvale / Santa Clara		41-TCCM-200-B.pdf
42 to 43	Santa Clara		42-TCCM-200-B.pdf
43 to 44	Santa Clara		43-TCCM-200-B.pdf
44 to 45	Santa Clara		44-TCCM-200-B.pdf
45 to 46	Santa Clara / San Jose	Santa Clara	45-TCCM-200-B.pdf
46 to 47	San Jose		46-TCCM-200-B.pdf
47 to 48	San Jose	San Jose Diridon	47-TCCM-200-B.pdf
48 to 49	San Jose		48-TCCM-200-B.pdf
49 to 50	San Jose	Tamien	49-TCCM-200-B.pdf
50 to 51	San Jose		50-TCCM-200-B.pdf
51 to 52	San Jose		51-TCCM-200-B.pdf
77 to 78	Gilroy	Gilroy	77-TCCM-200-B.pdf
78 to 79	Gilroy		78-TCCM-200-B.pdf

Peninsula EIS/EIR Announced

Sharp-eyed readers of the Federal Register will no doubt have noted in volume 73, number 249, pages 79541-79543 that the Federal Railroad Administration published a Notice of Intent on December 29th, 2008 to advise the public that FRA and the California High Speed Rail Authority will jointly prepare a project Environmental Impact Statement (EIS) and project Environmental Impact Report (EIR) for the San Francisco to San Jose section of the proposed California high-speed rail system.

The final peninsula impact evaluation is the next step in the tiered EIS/EIR process pursued by the FRA and the CHSRA, which already included the following milestones:

• 2005 HSR Statewide Final Program EIR/EIS
  
• 2008 HSR Bay Area to Central Valley Final Program EIR/EIS
• 2008 Selection of Pacheco Pass alignment

Highlights from the Notice of Intent for the peninsula:

This Project EIR/EIS will describe site-specific environmental impacts, will identify specific mitigation measures to address those impacts and will incorporate design practices to avoid and minimize potential adverse environmental impacts. The FRA and the Authority will assess the site characteristics, size, nature, and timing of proposed site-specific projects to determine whether the impacts are potentially significant and whether impacts can be avoided or mitigated. This project EIR/EIS will identify and evaluate reasonable and feasible site-specific alignment alternatives, and evaluate the impacts from construction, operation, and maintenance of the HST system.

(...)

The San Francisco to San Jose HST corridor selected by the Authority and FRA follows the Caltrain right-of-way from San Francisco to San Jose. The HST would operate in this area at speeds below 150 mph and would share tracks with Caltrain express commuter trains. Further engineering studies to be undertaken as part of this EIR/EIS process will examine and refine alignments in the Caltrain right-of-way.

The entire alignment would be grade separated. The options to be considered for the design of grade separated roadway crossings would include (1) Depressing the street to pass under the rail line; (2) elevating the street to pass over the rail line; and (3) leaving the street as-is and constructing rail line improvements to pass over or under the local street.

In addition, alternative sites for right-of-way maintenance, train storage facilities and a train service and inspection facility will be evaluated in the San Francisco to San Jose HST project area.

It all starts with a scoping process. You can comment orally or in writing at three public scoping meetings to be held this month. Mark your calendars:

• San Mateo County: SamTrans Auditorium, 1250 San Carlos Avenue, San Carlos, California, January 22, 2009 from 3 p.m. to 8 p.m.
• San Francisco: San Francisco State University, 835 Market Street, 6th Floor (Rooms 673-674), San Francisco, California, January 27, 2009 from 3 p.m. to 8 p.m.
• Santa Clara County: Santa Clara Convention Center, 5001 Great America Parkway, Great America Meeting Rooms 1 & 2, Santa Clara, California, January 29, 2009 from 3 p.m. to 8 p.m.

Written comments on the scope of the San Francisco to San Jose HST Project EIR/EIS should be provided to the CHSRA by March 6, 2009, and can be sent to comments@hsr.ca.gov with subject line San Francisco to San Jose HST.

Any suggestions for what should specifically be included in the peninsula EIR/EIS ? Please discuss in the comment section.