Capacity 101

Another sidebar to an upcoming post on Sepulveda Pass (soon, I promise!).

Revised based on some input from Paul Druce (@ReasonRail) and Alon Levy (@alon_levy).

You often hear opponents of rail transit like Randal O’Toole making preposterous claims about the capacity of bus lanes, like saying they can move over 100,000 passengers (pax) per hour. So here’s a short reference guide to the capacity of different types of infrastructure. We’re going to look at one lane or track in one direction.

Freeway lane (passenger cars): the capacity of a freeway lane is about 2,400 passenger cars per lane per hour (pcplph). Assuming an occupancy of 1.5 people per vehicle, that’s 3,600 pax/hr. If you assume that the cars are full, with 4 people per vehicle, and that driverless cars will allow headways of 1 second, that’s 3,600 pcplph and 14,400 pax/hr. As Alon points out below, a realistic occupancy for commuting is about 1.2 people per vehicle, or 2,880 pax/hr. I’m being a little generous with 2,400 pcplph too, the point being that even with generous assumptions, bus and rail have higher capacity.

Exclusive guideway (bus): a 60-foot articulated bus has a standing load of about 90 people and a crush load of about 120 people. If you assume one minute headways, that’s 5,400 pax/hr standing load and 7,200 pax/hr crush load. If you assume 20 second headways (or maybe more realistically, a three bus platoon every 1 minute) that’s 16,200 pax/hr standing load and 21,600 pax/hr crush load. This is a pretty aggressive assumption for bus operations, and labor costs would be high, but it might be doable with an exclusive ROW and good dispatching.

Exclusive guideway (light rail transit – LRT): LACMTA’s design criteria specify a full load of 164 people and a crush load of 218 people for a light rail vehicle. A reasonable assumption for minimum headway on LRT is about 2 minutes, or 30 trains per hour (tph). Metro specifies a design headway of 100 seconds and an operational headway of 2.5 minutes. With CBTC, 2 minute headways are easily achievable. For three-car trains, like LACMTA runs, that’s 14,760 pax/hr full load and 19,620 pax/hr crush load. Go with four-car trains, and that bumps you up to 19,680 pax/hr full load and 26,160 pax/hr crush load. If you could drive headways down to 90 seconds (about what the slightly dysfunctional MBTA Green Line runs), you could get 40 tph for 26,240 pax/hr full load and 34,880 pax/hr crush load.

Exclusive guideway (heavy rail – metro): LACMTA’s design criteria specify a full load of 180 people and a crush load of 301 people for a heavy rail vehicle. Headway assumptions are the same as for LRT. For six-car trains at two minute headways, that’s 32,400 pax/hr full load and 54,180 pax/hr crush load. For a ten-car train at two minute headways, 54,000 pax/hr full load and 90,300 pax/hr crush load. Get it down to 1.5 minute headways and it’s 72,000 pax/hr full load and 120,400 pax/hr crush load.

Here’s a summary table.

capacity

Note that even at this level, we’re not playing fair between rail, bus, and auto. Rail capacity is effectively limited by the signaling system and other regulations like NFPA 130. Bus and passenger car capacity is limited by station capacity. Berthing a train every two minutes is a breeze. Berthing a bus every 15-20 seconds is very difficult, even with long platforms. Berthing a passenger car every 1.0-1.5 seconds is impossible.

So how do people like O’Toole get outlandish capacities like 110,000 pax/hr for bus, while claiming rail has capacity below 10,000 pax/hr? Easy, posit a bus system that doesn’t actually work, and cleverly sandbag rail.

On the bus side, O’Toole assumes a capacity of 1,100 buses per hour or about one every 3 seconds. That works great as long as no one ever has to stop. You could only operate a bus lane at that volume if it was just a trunk that many bus routes used between their origins and destinations, much the same as how cars use a freeway. Think about it: if you were running 1,100 buses per hour on the 405 and 1,110 buses per hour on the 10, you could never hope to have transfers between the lines. You couldn’t operate transit lines, only point to point services, or lines with no stops or transfers between them on the trunk.

On the rail side, O’Toole assumes 3 minute headways, versus our 2 minute headways. What’s a minute among friends? Well, going from 3 minutes to 2 minutes increases capacity by 50%. If you run with CBTC and get 1.5 minute headways, that’s twice as much capacity as O’Toole calculates. In other words, when headways are low, small differences in headway make a big difference in capacity.

At high passenger volumes, rail is still the best option, offering lower operating costs and better reliability. It’s easier to run trains at 2 minute headways than buses every 15 seconds. For lower passenger volumes, bus is often fine, but remember that, as Jarrett Walker says, the most important things is the quality of the ROW. Few cities need to move as many people as the Lexington Av subway in New York. Start with a high quality ROW, then pick the mode that’s the best combination of cost effectiveness, compatibility with existing systems, and accommodation for future growth.

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17 thoughts on “Capacity 101

  1. Alon Levy

    The numbers you give for cars aren’t really right, because for urban commute travel, there’s very little carpooling. In the US, the average occupancy levels are about 1.2 for commute trips and 2 for intercity trips. Assuming 4 people per car is a fantasy for first-world urban travel.

    Reply
    1. letsgola Post author

      Yeah, the idea was to be generous, & note that even with generous assumptions, you still move fewer people. I updated the post to include a capacity for 1.2 pax/vehicle and note the generous assumptions.

      Reply
    2. Zmapper

      1. It is wrong to compare the theoretical maximum capacity of one mode to the empirical average capacity of another. If rail and BRT is to be looked at through theoretical maximum capacity, then cars are to be viewed the same as well.

      1.5. People do more than commute to work, even during rush hours. The 1.6 figure is an average incorporating all trips. In certain cases, even higher empirical average occupancies are achieved; HOV-3/4 lanes (I-95 approaching DC) or busy intercity highways with a strong weekend peak (I-70 west of Denver) have very high average occupancy levels and are often congested.

      Reply
      1. Alon Levy

        It’s not quite theoretical maximum, so much as practical maximum during the peak. Cars tend to be less full during peak commute hours because of drivers’ tendency to drive alone; the car trips one can do with the entire family tend to be off-peak.

      2. bbqroast

        1) We are talking about maximum capacity here.

        Putting a motor way at max capacity does NOT increase car occupancy.

        There’s no benefit to car pooling, in fact everyone wants to “get ahead of the traffic”. Even with T2< lanes it's difficult to get people into other people's cars.

        With MRT on the other hand, people will crush in to the train as much as they can, as someone has an incentive to do so (because they get to their destination faster).

  2. Matthew

    The Lincoln tunnel XBL is basically that non stop bus segment carrying many thousands of people per hour.

    Of course it requires an enormous, overflowing terminal to berth all those buses. Then they have to be squeezed back out to NJ for daily storage.

    Reply
    1. letsgola Post author

      Yes, you need that huge terminal, and there’s no transferring between the services (or in-line stations). A bus lane at that volume is really not comparable to a local bus line or a rail transit line.

      Reply
    2. Alon Levy

      It’s so easy to focus on the cost of the link and forget the cost of the stations. Second Avenue Subway’s stations are about 75% of the cost of Phase 1. With BRT, the problem gets worse, because there need to be additional lanes for stations, or else buses would have to stop on running lanes and capacity would go down to a bus every 3 minutes. And then there are the junctions. With urban rail, this is the simplest: people get off the train at a junction, walk to the platform of their connecting train, and board. Mainline rail, which involves longer trips, sometimes with luggage, tends to favor cross-platform transfers, but usually these already exist on the legacy network. But road transportation’s capacity goes down crashing if people ever have to exit vehicles, which forces junctions to be humongous and completely unaffordable in the dense urban settings that generate the most traffic.

      Reply
  3. Shane Phillips

    Wait, are you telling me that Randall O’Toole used misleading numbers in order to make a point based on his preconceived notions and political biases rather than relying upon empirical facts!?!?

    Reply
  4. Darrell Clarke

    Thanks for emphasizing the error of bus capacities measured where buses don’t stop!
    For cars in a freeway lane I use a lower number of around 1,300 vehicles per lane per hour that occurs with congested flow — the standard condition in Los Angeles. Multiply by 1.2 people per car for a result of slightly over 1,500 people per lane per hour.
    Twenty-second headways for buses seems awfully close, considering that light rail dwell times alone are 20 seconds, as I measured once on the Blue Line.
    At the Blue Line’s current 6-minute headways and a moderate 100 people (3/4 seated) per car that is 3,600 people per hour per track, equaling over two freeway lanes. The Regional Connector is being designed for two lines at 5-minute headways each (about the limit for at-grade crossings beyond the Connector), or 2.5 minutes combined.
    BART on peak runs twenty 10-car trains per hour per direction through the trans-bay tube, which I once calculated exceeded the capacity of one 5-lane direction of the Bay Bridge.

    Reply
  5. Zmapper

    Transit vehicle capacity as often presented is misleading. In practice, crush-loaded 40′ buses do not carry 70 people, nor do 60′ carry 100 or more.

    Scheduled transit capacity in the majority of transit agencies is dictated by a load factor, itself based off of the interior seat count. Typically, for busy routes a peak load factor between 1.25 and 1.5 is used; Los Angeles Metro uses 1.3. Off peak, service is planned so that in theory, on average nobody has to involuntarily stand (given customer behavior this usually means that about 3-5 people are standing by the rear door but 3-5 seats are empty).

    Now, the obvious solution to increase capacity is to remove seats; two people or so can stand in the area one seated customer requires. The problem is that while the percentage of customers standing increases, and in theory a few more customers can board, the percentage of customers willing or able to stand comfortably does not increase. As many trips on local bus networks are relatively long, standing is considerably worse than sitting, and is likely a significant push factor discouraging ridership. In the near future, a greater percentage of riders on CANZUS systems are also likely to be older and less mobile, with an even stronger preference for seats over standing space. Increasing the policy load factor appears to create more capacity, but this is only a short-term relief; the proper long-term solution is to schedule enough service to meet demand at an acceptable load factor.

    Of course, if space is the scheduling constraint, then a problem exists. Unless and until buses are scheduled less than one to two minutes apart, this doesn’t apply. If it does, your cities’ next challenge is constructing a higher capacity mode to accommodate demand levels the vast majority of transit agencies would dream to have as a “problem”.

    Mixed-traffic streetcar boosters love to focus on theoretical capacities over acceptable policy capacities, thinking that customers will accept uncomfortable situations for extended periods of time because they aren’t on a bus (the most common model, the 66′ long United Streetcar 100, has fewer seats and significantly more standing room than a low-floor 40′ bus). Unfortunately for them, ridership increases include customers both willing and unwilling to stand; you don’t to select away and discriminate against certain “problem” customers unwilling or uncomfortable standing for extended time due to young children, shopping bags, health issues, the elderly, the disabled, etc.

    Reply
    1. letsgola Post author

      The numbers presented in the post are indeed on the high side, leaning towards theoretical capacity. As you say, the practical capacity for the line will be affected by agency policy. It will also be impacted by uneven distribution of demand along the route, i.e. the vehicle will not be at maximum load for the entire trip, so you’ll always be moving fewer people than theoretically possible based on the amount of service you’re providing.

      For comparisons between different modes, the results are more or less the same, because the post also includes some optimistic assumptions about freeway lane capacity and car occupancy. It would be difficult to achieve 2400 pcphpl in practice even without the weaving impacts of cars exiting the freeway, entering the freeway, and changing lanes. Likewise, the freeway capacity will determined by choke points, and in the same way you won’t fill a bus for its entire run, a freeway won’t be flowing at capacity for its entire length.

      Reply
  6. alexfrancisburchard

    I think this is awesome, I’ve run similar numbers myself and come up with roughly the same things, but I would like to mention that Istanbul Turkey has a BRT Line (the metrobus) that has busses every 14 seconds for parts of the day, and they run single and bi-articulated busses. I believe the line carries 750,000 people per day.

    I also believe that they are wasting a TREMENDOUS amount of money because if they just threw rails into the busway they’d save piles of money because they could run one train every 3 minutes with 1 driver instead of 13 busses in that time

    OTOH though, Never waiting more than 30 seconds for a vehicle to show up is WICKED awesome. It’s like having a car honestly.

    Reply
  7. Pingback: Sepulveda Pass Transit, Part 3: Mode and Alignment Through the Pass | Let's Go LA

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