12 August 2017

Freeway Lanes of Caltrain

If everyone drove instead of taking Caltrain, how many more lanes would peninsula freeways need to absorb the additional traffic?

The way to answer this question is to count how many train passengers ride past any given location, in each direction, within the span of one hour. Caltrain publishes all the information you need to do this calculation rigorously, without making any assumptions: the timetable tells you when each train passes each location, and the 2016 weekday passenger count by train tells you how many people are on board that train at that time.

Four cases are considered: morning northbound, evening northbound, morning southbound, and evening southbound. Rather than picking a fixed morning and evening hour over which to count passengers, we slide a one-hour window across the peak period until we find the peak hour at each location, during which the most passengers ride past. Caltrain operates five trains per hour per direction repeating on an hourly cadence, so we never count more than five trains in the totals.

It is an easy but tedious calculation, perfectly suited for a computer.  This is what pops out:

This graph reveals many of the features noted in ridership reports: the flow is asymmetrical with more riders traveling northbound AM / southbound PM, the Gilroy branch is dead, Stanford generates enormous ridership, etc.

Translation to Freeway Lanes

To convert the number of Caltrain passengers into freeway lanes, very few assumptions are needed, and those we need can be backed up by references.
  1. A congested freeway lane operating at 45 mph can carry 2000 passenger cars per hour, according to the Federal Highway Administration's HPMS Field Manual (Parameter values: FFS = 45 mph, BaseCap = 2150 pcphpl, PHF = 0.95, fHV = 0.98, fp = 1.0).
  2. The average vehicle occupancy (AVO) is 1.3 people, based on two studies of the 101 corridor in San Mateo County. This figure includes buses, van pools and corporate shuttles.
This means a single freeway lane can theoretically carry 2600 people in one hour. Note this is a very optimistic figure because slight perturbations in the flow of traffic can cause slow-downs that reduce throughput due to lower free flow speed (FFS). But we'll use this very high number to make an extremely conservative estimate of how many lanes of freeway can carry all of Caltrain's ridership.

Freeway lanes typically do not change directions to accommodate peak flows. That means we must consider northbound lanes separately from southbound lanes, with no possibility of re-allocating the lane capacity to accommodate the AM/PM flow asymmetry that is observed on Caltrain. In practice, this means we must add the northbound peak flow (AM or PM, whichever is highest) to the southbound peak flow (again the highest of AM or PM) to size the number of equivalent freeway lanes. Looking at the graph above, which shows the highest flow is northbound AM and southbound PM, we must add AM northbound and PM southbound people per hour, and divide by 2600 people per hour per freeway lane. Here is the result:

So as of 2016, plain old diesel Caltrain equals about 2.5 lanes of freeway, including both directions. If you integrate the area under this curve, you get how many lane-miles of freeway would be needed to replace Caltrain. That number is 119 lane-miles. These are very conservative lower bounds.

When you hear the argument that "millions" of people use highway 101 but only about 30,000 people use Caltrain, shut it down with facts: today Caltrain amounts to 2.5 / 8 or at least 30% of the lane capacity of highway 101 during rush hour. The reply might be that not all those people would end up on 101, but with an average trip length of 23 miles, which driver wouldn't use a freeway?

Future Capacity Implications

Caltrain capacity is set to increase considerably, first by ~30% with the initial electrification and modernization project, and by ~60% once the system is running at 6 trains per hour with 8 cars each. (If you don't count standees, those figures are ~10% and ~25%, but why would you not count standees?) A 60% capacity increase is equivalent to one and a half lanes added to the entire length of highway 101 from San Jose to San Francisco.

It doesn't have to stop there: more trains per hour and longer trains are possible, because EMU trains scale up in a way that diesel can't. A future Caltrain capacity increase to about 10,000 passengers per peak hour per direction (about triple today's throughput) isn't out of the question, does not require adding tracks or expanding the rail corridor, and would equate to adding 5 new freeway lanes.

In certain quarters of Silicon Valley that are enamored of Hyperloops, self-driving Teslas and Boring underground tunnels, electric Caltrain is looked down upon as a last-century technology that is about to be made obsolete. That particular outlook fails to grasp the importance of throughput or to recognize the enormous carrying capacity of modern electric rail. Self-driving Teslas and Hyperloops will achieve dismal throughput capacity as measured in passengers per hour, and no amount of whiz-bang technology will change the underlying geometry of this increasingly urban region.

The way forward is to add more freeway lanes of Caltrain.