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Estimating Passenger Throughput Capacity of PRT Technology

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Estimating Passenger Throughput Capacity of PRT Technology


Much confusion exists about PRT's capacity to move people. Many jump to the conclusion that small vehicles cannot move as many people as large vehicles. Perhaps the analogy of cutting a log with an ax vs. chainsaw will help. Although ax heads are large with a big cutting edge, chainsaw cutting teeth are small. Yet, professionals prefer those many small chainsaw teeth to the ax.

As with heavy freeway traffic, we can space computer-controlled vehicles 1 second apart. Even if each vehicle contained only 1 passenger, each PRT guideway could deliver 3600 (60 vehicles per hour X 60 minutes per hour) people per hour (p/h) – or 86,400 (3600 p/h x 24 hr) passenger per day (p/d).

1 podcar/second = 3600 people/hour = 86,400 p/d for each guideway direction

In the interest of accuracy, maximum possible throughput numbers should be reduced about 50% as noted in the October 17, 2012 memo (page 5) from Hans F. Larsen to the TRANSPORTATION AND ENVIRONMENT COMMITTEE regarding the AUTOMATED TRANSIT NETWORK FEASIBILITY STUDY:
Realistically, throughput for an ATN is likely to be much less – perhaps even less than half – of what would be indicated from an idealized capacity calculation derived from simple line-haul formulas.
Let's apply a realistic throughput factor of 50%. That yields 43,200 p/d per guideway, or 86,400 p/d for both directions.

(86,400 p/d for each guideway X 50%) X 2 directions = 86,400 p/d

86,400 p/d compares well with the 55,000 p/d that VTA projects for the BART Burrow in 2040.

If necessary, capacity could be doubled by building parallel guideways.

Even doubling the estimated PRT system cost to replace the BART Burrow from 4% to 8% is still a bargain. VTA is urged to assess the opportunity costs of spending 12 to 25 times more than necessary to connect the Berryessa BART station with downtown, Diridon Station, and Santa Clara. We can do better.



One PRT company (MISTER/Metrino) has published a capacity throughput analysis:
http://metrino-prt.com/wp-content/uploads/2014/08/MISTER-Capacity-Thruput-analysis-12-TL.pdf

It appears that using a 0.7s headway at 50 km/h (31 mph) yields 5,000 vehicles/cabs per hour on a guideway.
Applying a 1.3 occupancy factor yields 6,500 people per hour transported on a single guideway.




In the real world of Morgantown, WV, the PRT/GRT system built in the 70's provides about 15,000 rides a day (and double that when WVU has a home game). (A single trip on the Morgantown PRT costs just 50 cents, and is free for students.) According to a recent report, the University would need anywhere from 30 to 60 buses in loops, running nonstop, to transport their students.




The Advanced Transit Association (ATRA) presents another way to see capacity as outlined in this ATRA article which includes the chart below:

As shown, commuter rail like BART can handle 35,000 to 60,000 people per hour (one direction). However, VTA estimates that 55,000 people per day (p/d) will use the BART Burrow in 2040. Clearly, BART is oversized for the demand. PRT, with a capacity of 3,000 to 5,000 people per hour, is scaled appropriately for the BART Burrow route.

Here is a similar capacity graph done by the Modutram folks in Guadalajara, Mexico, who are developing the Autotrén PRT system.




What about crowds?

Some people question the use of Personal Rapid Transit (PRT) to handle crowds of people. To them, it seems obvious that small PRT cabs simply cannot handle heavy loads such as when a commuter train stops at a station or a stadium crowd leaves. In the case of commuter rail (Caltrain and BART in the San Jose, CA area), consider these points:

  • Only a portion of people getting off the train at a station would want to use PRT service rather than other options (walk, bike, electric scooter, taxi, bus, Uber, friend, etc.).
  • Not all of those who do want to use PRT will transfer within the same 60-second timing window; rather they will be spread out over a few minutes.
  • Multiple PRT loading areas operated in parallel can handle stadium-sized crowds, so a crowd getting off a train is easy.

On the "world's best general-knowledge PRT website", the subject of capacity is well-covered. Additionally, the particular problem of demand bursts such as when a stadium empties ("But what about crowds?") is examined. Using their estimate of 15 seconds as the average time between PRT departures, 10 berths would be required to clear 120 people in 3 minutes (4 people/min/berth X 3 min X 10 berths = 120 people). It's likely that 2 stations (with 5-7 berths each) would serve BART and Caltrain stations. If more than 120 people want to exit the station via PRT (instead of the other available options) - or 3 minutes is deemed too long - additional stations could be built for less than $1M each.

Copied from an e-mail:
As for "low capacity" of podcars, this is only true for a system which has too few stations or bays. Coincidentally I went over the math with one of the students this afternoon before seeing this message. In a system with 1 station and a single position ("bay") for only one podcar at a time -- a classic corridor in other words, not a podcar network:
3600 seconds/hour ÷ loading time ≥20 seconds ⊗ ≤6 people in a podcar ≅ 1000 pax/hour.

Not great. So adding stations, plus stations with multiple bays, today the student and I calc'd max potential throughput:
3600 secs/hr ÷ 1 sec/car ⊗ 6 pax/car ⊗ 15 hrs operational per day ≅ 324,000 pax / day >> BART (etc.) at about 100,000 per day.

One second intervals? Well that's far more generous than the space between my rear bumper and the front bumper of the $%^@!{&* behind me on highway 17, and is the standard being developed by the person who designed the controls for the Morgantown PRT in the 1970's and was head of R&D for BART till a few years ago.

Of course this best case wouldn't be reached in practice, so let's be extremely conservative and say this is off by a factor of 10. Well, since costs are 10X less than light rail and 20-50X less than subways (proven by PRT prototypes I've seen in action, including the one I rode last week), then 324,000 ÷ 10 = 32,400 ⊗ factor of 10 savings = 324,000 pax per day -- back where we started: at least 3X more throughput than any other alternative given the same budget.

Additional Notes on System Capacity (passengers per hour per guideway)

Can small cabs move large numbers of people like traditional mass transit? Yes. Uninterrupted flow is the key to capacity, not vehicle size. For example, 60-passenger buses arriving two minutes apart (a very high flow rate for an American bus system) can carry 1800 passengers per hour. PRT vehicles coming every two seconds can provide the same capacity.  PRT capactiy depends on headways:

  • 0.5 second = 120/min or 72000hr
  • 0.6 second = 100/min or 6000/hr
  • 2.0 seconds = 30/min or 1800/hr

A commonly accepted safety zone on roadways is 2 seconds between cars. Although automatic control of PRT cabs is safer and more reliable than human drivers, let's assume our PRT systems starts with that comfortable two seconds of space between each cab, aka "headway". At that headway, 1800 cabs per hour can roll down the guideway. That's 1800 people per hour assuming sole-ridership will prevail (30 cabs/min * 60 mins/hour = 1800 cabs per hour). That approximates the maximum volume of a freeway lane of traffic (2200). After a few years of operation, we may have the confidence to reduce the headway times to only one half second. That would quadruple throughput to 7200 cabs/hour. Now we're talking the volume of three freeway lanes in less than the space of one physical lane.

Now, compare that volume to LRT and trains. Although LRT systems may be designed for high volume, the actual limit of any operating LRT system in the U.S. is 1200 riders per hour; peak  in Sacramento is about 1000 passengers/hr.  Likewise for trains where the theoretical limit is 20,000 riders/hour, actual loading often tops out near 7000 riders/hour. An exception may be BART where reports indicate near-saturation of the trans-Bay tube at 20,000 riders/hour [is that one way, or both?].

Another capacity comparison could be made with computer controlled cars as demonstrated near San Bernadino, CA.  Partners for Advanced Transit and Highways (PATH) ran Buick Le Sabres by computers on a dedicated strip of freeway with magnets embedded so the cars could be computer controlled. They ran for thousands of miles at 60 mph with 0.25 sec. headways.  Some of PATH's research, particularly its work in the Advanced Vehicle Control Systems area, has been covered by a range of media. http://www.path.berkeley.edu/PATH/Publications/Media/ More recently, Hundai has demonstrated even more control of vehicles at speed.

Speed is another factor in capacity. Here are critical ideas from PRT pioneer Ed Anderson:

Subj: RE: [prt-talk] Digest Number 56
Date: 5/27/01 5:32:19 PM Pacific Daylight Time
From: jeanderson@taxi2000.com (Ed Anderson)

You mentioned some of the system problems. Tires vs. maglev are not the most important considerations. Curve radii increase as the square of the speed and off-line guideway lengths increase in proportion to speed. These are the most important factors. Life-cycle-cost per passenger-mile is the annualized capital + operating cost divided by the annual ridership. Costs increase with speed regardless of the means of suspension and ridership will increase with speed to a point. After a certain speed, costs increase faster than ridership so the cost per passenger-mile increases. - JEA

So, pick a speed that ensures high ridership by offering 1) a low cost per passenger-mile and 2) speeds that compete with the automobile . Absent any analysis, I pick 40 mph. Let's start engineering with that operating speed in mind.

Here's some capacity numbers from the bike folks: It takes three lanes of a given size to move 40,000 people across a bridge in one hour using automated trains, four to move them on buses, twelve to move them in their cars, and only two lanes for them to pedal across on bicycles.

A vehicle at a red light requires about 240 square feet of space (that's a standard 12-foot lane with a standard 20-foot long "envelope" per car). At 20 mph, it requires about 700 square feet.  And for a car zooming at 40 mph, the number balloons to about 2,000 square feet.  Maximal traffic on a highway lane runs at 2.2-second intervals.  At 10 mph that is 1000/hr; at 30 mph about 1500/hr.  It never gets more about 1500/hr because the vehicle grows with velocity.  At 50 mph,  a car is 1,285 feet long.  PRT capacity or speed does not decrease with a heavy load; at 2 second headway, it will have 3 times the capacity as a landeof traffic, and at 0.5 second headway, it will have 12 times the capacity.  



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