Saturday, April 20, 2013

155> For Example...

One of the problems with PRT is that it requires a network to function at its full potential, and cities and investors alike are reluctant to fund such a complex, untried undertaking.  Unfortunately a small, trial loop reflects nothing about how a bigger system would work.  It’s like giving some pickup trucks and a circular track to Amazonian tribesmen.  Vehicles are only as enabling as their routes will allow.

I have, for this reason, given particular focus on the problems of minimal networks, since this will always be the starting point, like it or not.  Configurations such as a single loop, unfortunately, do not make a very compelling case for PRT when compared to more traditional alternatives.  Yet this is a battle that should not be ceded, because businessmen need the prospect of near-term profits as well as hopes of a long term bonanza.  Therefore a design that is superior in this respect is the more lucrative offering.  
To illuminate this point, let’s consider a starter loop with, say, four stations.  Our imaginary system goes 35 mph, and has one second headways between vehicles.  Let’s further stipulate that the stations are in pairs, say two stations downtown and a pair two miles away, say, in a hospital/hotel district.  This is so we can better count the passengers, who will be assumed to be traveling between the two main areas, making a two mile trip.

That means that at maximum capacity, a vehicle will come into one of the two stations at the end of the loop every second, so if there is full, equal demand, there will be an arriving vehicle at each station every two seconds.  That means, to keep the whole thing going, there must also be a vehicle leaving each station every two seconds as well. 

That is challenging logistically.  In order to have a vehicle leaving every two seconds, there will need to be many people boarding a large number of vehicles at once.  For example, let’s suppose it takes 30 seconds to get access and get seated.  There will need to be 15 parties boarding simultaneously, just to keep up.  There will also be 15 parties leaving the vehicles – hopefully a bit faster, let’s say 20 seconds.  Let’s say there is a 10 second delay between people leaving and people boarding. (After all, at least sometimes the vehicles will have to move up.)   That means that if each vehicle is in the station for only 60 seconds, the station will still need 30 births.  And that is with everything working like a clock.  

With this in mind, I decided to construct a model of the track layout for such a station.  In the illustration below, vehicles in the rear would be letting people out, while the front vehicles would be loading.  This design enables loading of the fifteen vehicles at once, so that the one-vehicle-per-two-seconds rate can be achieved.  Note that with a suspended system, passengers can walk to vehicles without crossing tracks – an advantage over designs with the wheels at the bottom, which would require the passengers to change levels to avoid crossing tracks.

Unlike these illustrations, obviously such a station would be a beehive of activity, and everything would have to be working perfectly to get those vehicles in and out in sixty seconds!  I imagine that there would be green and red lights and self-locking gates to regulate access to the vehicles.

For the curious, here are some additional, extrapolated numbers.  35 mph = 184,800 feet per hour = 3080 ft. feet per minute = 51.3 feet per second, which gives us our headway distance.   At this full capacity there are 102 vehicles on each mile of track, or 204 each way on our two mile example.  If there are always 30 in each station, that equals 120, so 204 x 2 = 408 +120 = 528 separate vehicles.

It is easy to see how people would regard PRT as hopelessly impractical after reflecting on these considerations.  After all, a single light rail train can carry 400 people at once.  Let’s do the math.  If each pair of stations does, indeed, deliver a vehicle each second between them, that is sixty per minute, or 3600 per hour.  Assuming something like the 1.2 passengers per vehicle average that is common for auto traffic, that is 4320 passengers per hour, each way.  That is just over what a four-car light rail train can carry with just ten trips per hour, or one train every six minutes.  Buses, on a designated “busway”, running with headways of about a minute, can also boast similar capacities.  Either seems much easier than PRT.

But let’s look at the other side of the coin.  First of all, where can you find enough pedestrians to even walk through the doors of such a station at that rate for more than a couple of hours a day?  Disney World? Niagara Falls?  It will be far more typical to spread the load out with more, smaller stations.  So this example greatly favors large capacity vehicles.  Furthermore, in such a “back and forth” layout, it would be highly unlikely that people would want to pay a premium for a private vehicle for such a short trip.  It would be a simple matter to use at least 75% of them as shuttles, at a fraction of the fare, taking four passengers at a time.  That boosts capacity to almost 12000 passengers per hour. Use of GRT (group rapid transit) vehicles would probably result in still higher capacities, although headways would have to be greater, and track would have to be beefier as well.

The cost for light rail is phenomenally high, like 60 million USD per mile just for the track. Compare that with the often quoted estimate of 15 million per mile for PRT, and it’s pretty easy to see where the money for all of those vehicles could come from!

Adding only a few additional stations starts to really break down the advantages that buses and trains enjoy.  These large vehicles are slow to start and stop, dropping their round-trip speeds down with each new station. (On the other hand, 35 mph is conservative for PRT, especially for the SMART system depicted, which can easily achieve highway speeds and is designed to mitigate G forces)  Large transit vehicles block traffic, and are very expensive to elevate to avoid this.  Every stop inconveniences the vast majority of passengers who not boarding or getting off.  Once there are a dozen or so stops, it’s really a mess.  From a simple perspective of real estate usage, large vehicles MUST accommodate large crowds to justify their presence.  The advantage of scale (of LRT and BRT) becomes a disadvantage when it comes to offline stations or other means of passing.  In fact, it could be argued that even simple bus stops, in congested areas, often do more harm than good.  While the bus is stopped, or is nearly so, it is using valuable real estate that could better be used for facilitating the flow of ordinary traffic.  This is especially true if there are only one or two passengers using that stop. With light rail a similar condition exists.  Every stop must justify the wait for all through-passengers, as well as pedestrians and vehicles that would otherwise be able to cross the tracks.  Therefore light rail should have as few and as large stations as conditions will permit. How few and how large?  That is debatable, but it seems to me that holding up 400 passengers to let a dozen or so off and on is real waste.  This certainly gives a clue as to how to make these heavier forms of transit more effective.  It seems that there should be a limit on how small of a station should be permitted, as well as a limit on the number of stations, period.

I think this raises an interesting question, particularly in regard to light rail.  Could PRT actually be good for this form of transit instead of competing with it?  Let’s start with some parameters. Say we want to limit  the number of stops and increase the passenger usage at those stops so that there is no less than 10% turnover at each stop, with 10 stops total on a loop, so most passengers would only have to wait through 5.  If the train has a capacity of 400, that is an exchange of 40 at each stop.  Let’s say that we want to provide the convenience of a train every 5 minutes.  That’s 480 pedestrians boarding at each stop per hour, or 8 “walk-ups” per minute.  Even this, except for rush hour and perhaps lunch time, seems like a lot for most areas.  Could PRT be used to deliver those passengers?

It’s a provocative notion.  After all, light rail is often run at less than capacity, and is generally constrained by the lack of routes with sufficient riders to justify its enormous cost.  It would seem that they might have much to gain by offering a more global transportation solution.  Do light rail venders even suggest multi-modal approaches?  For example it would seem like a no-brainer to link “park&ride” buses with certain light rail stops.  After all, in order to have good geographical coverage along a route, there are liable to be some stops that bring in fewer passengers. Why not make such non-performers into interfaces with other systems, like buses or PRT?  That way every station is worth the time and trouble, every time.

Of course this raises the question of why someone would take the LRT of BRT at all, instead of simply taking PRT the whole way.  I suppose I have given a bad example here for making the case for switching modes, particularly in that my example involves short distances and slow speeds.  I have always believed that PRT is most valuable and viable at the upper speed and distance ranges, at least by traditional standards.  As such, PRT networks would first connect important hubs within a city, instead of growing out from the center, as is usually supposed.  True, using PRT instead of heavier transit in situations like the one I have outlined would be a viable alternative in the first place, but we are just not there yet.  Our time will come, but in the meantime, LRT venders might do well to offer both options.  Smart business people know when it’s time to cannibalize sales of older mainstay products with more modern offerings.  This transition could be made less painful if the switch is to a product/service that is complementary in the meantime.  The move to networked transit systems will only hurt companies that are entrenched in the “line-haul” business model. Meanwhile, PRT developers must design for transit problems that other systems can’t solve.  Just being “networkable” does little good when cities are only in the market for a loop.


Andrew F said...

Dan, I agree that in many applications where LRT is proposed, PRT could compete strongly. Partly this is due to the fact that LRT is not economical in many of its applications, but used anyway for ideological reasons. There are many LRT systems where even at peak times, the line operates at 10 - 15 headways without full vehicles.

I'll also note that you 30 berth station with vehicles departing every 2 seconds, 1800 vehicles an hour, this station would be able to handle peak passenger demand at quite a few subway stations in Toronto with even an occupancy of 1.2. If operated in GRT or partial GRT mode to get occupancy up to 2.5 - 3.5, you'd be able to match all but the 20 busiest stations.

This is impressive, because I would think the station you depict could be built for no more than a few million, including a canopy to protect from rain. It could be built on a concrete pad on a streetcorner This compares favourably to the $100 million+ it costs to build subway stations.

As far as PRT supporting LRT development, I just can't see it. Any application where the demand is just too high for PRT to serve calls for heavy rail transit on grade-separated ROWs. Although, really, some of the GRT system, even if you ran it underground, might work as well for lower cost. Where demand is not too high for PRT, why would you both with big, slow, expensive and land-consuming LRT? Any incremental transit investment would be better spent in increasing the scale of the PRT network, to gain the network effects.

Asko K. said...

Great write, I hope some LRT people see this and start approaching companies that can provide added coverage for their tracks.

New Delhi metro is one example. Underutilized, not living up to the original calculations. A good feeder system can change that.

btw, What did you mean by:
"Note that with a suspended system, passengers can walk to vehicles without crossing tracks – an advantage over designs with the wheels at the bottom, which would require the passengers to change levels to avoid crossing tracks."

Don't think that is valid for all supported systems.

Andrew F said...

I guess I should qualify that existing LRT may make sense to base a feeder system around--but only because the cost of the LRT is sunk. New deployments of LRT are doubtful investments.

I did a basic investigation of a feeder system into a subway terminus in Toronto, partly because there are ridership figures for the bus routes that currently perform that function. An even better application would be to link to an activity centre that is not currently connected to the subway network.

Andrew F said...

Off-topic, but I thought you might be interested, Dan.

Here's a video about a protocol for autonomous vehicles negotiating reservations for intersections to avoid collisions. The interesting thing, which the speaker does not allude to, is that this would work well for PRT. Actually, it would work much better for PRT than it would for cars, given a guide-way captive vehicle has fewer degrees of freedom, 100% autonomous vehicles, and no other modes (pedestrians) to contend with.

Dan said...

Actually, Andrew, I did the design to illustrate an example of PRT being at a disadvantage. I do think the station has an awfully big footprint, and I think I was a bit optimistic on throughput. I am, however, trying to build a library of 3D track components that are compatible with my latest vehicle iteration and this gave me an excuse to create them. Also, since many readers have probably have not read my earlier posts on parallel boarding, I thought I might re-introduce the concept.

As to the viability of PRT being a feeder for LRT, I may have been influenced by events down in Houston, where they keep floating proposals for new routes and they keep getting voted down. From the perspective of the frustrated vender, it would seem that they would want to A] Have a way to ensure higher (and earlier) ridership/fare numbers, B] Have a way to offer a geographically more comprehensive solution, or C] Have an alternative product to offer, thus getting a second chance to bring in a sale. This way, instead of just being an LRT company, they could be a “transportation solutions” company. I’m sure the dynamics vary a lot, place to place, however.

And thanks for the video. I always appreciate relevant links! I did one post, a while back, where I outlined a “reservation” system for merging semi-autonomous PRT vehicles, whereby each vehicle would “reserve” the merge point for its estimated time of arrival. These “reservations” would then be continuously renegotiated between the vehicles involved, until each got the best deal possible. This is almost exactly like what he is doing with the grid, except his job is much, much more complex.

Asko, I had to think about that one… Maybe I didn’t make it clear that I was talking about stations with parallel tracks… (Is there any other way to have vehicles departing at such a high rate?) I confess I haven’t given as much thought to supported systems as suspended ones… And yes, I can see now that by allowing supported vehicles to cross paths this limitation can be overcome. This could be done by routing the vehicles over and under, if the ramp lengths can be accommodated, or, since the whole thing is controlled by computer, it could be done on a single level with very little delay, as in Andrew’s video. Is this what you are referring to? Another option, which would seem to allow fast departures without (one way) parallel tracks would be to turn the vehicles around in the docking bay (or have little turn-around loops) or simply have bidirectional vehicles. Thus there would be no blockage while a vehicle backs into the exiting track because it would be going forward already. Or am I still missing something?

Andrew F said...

Sorry, Dan. I acknowledge that the situation you described was the ideal for a linehaul big-box transit system and how PRT could deal with the same situation. It seemed to me that your point was that PRT could serve in that application, albeit with some largish (for PRT) stations. I know that in practice, PRT would have more, smaller stations.

I do, however, think that stations on the scale you depict would exist in a mature PRT network in high traffic areas where the station density would become too high if served with small stations. The canonical example is a sports stadium after a game, though GRT would probably be warranted in that case.

I think you might have a hard time convincing existing transit system makers. If it helps them sell high cost, high margin transit systems, you might get their attention. In the end though, the customer you have to convince is the city transport planning authority. Offering PRT as an augmentation to LRT helps it to get its foot in the door for tenders that are structured so that the only acceptable proposal is LRT. The problem is that it will inherently cost more than LRT-only, even if it delivers higher ridership and better service.

One way a supported system could avoid forcing passengers to change levels would be to use a series of sidings off the main station siding. This would make for a long station, and could result in more congestion, but it could be accomplished with a supported system. If vehicles have doors on both sides, you could have one series of sidings on each side of a single platform.

Anonymous said...

Great article, Dan!

I have thought of the same and I would start from a city with many bridges, wher traffic jams are there b/c of bridges (I have heard Stockholm is on 14 islands connected by 57 bridges). The cost of bridges vs. cost of PRT is more interesting and favours PRT. As to stations, sry, I thing the benefit of PRT is that is can and should be a door-to-door solution, ie. the getting on and getting off is far more distributed than for conventional public transport. Ideally, the pod can lower itself to street level and take on or leave people at any point where the track is! This is needed to compete with cars and solves also the uestion where park of these pods. This would require stations (with large footpint) only in airports and shopping centres and places like that. Maybe start with industrial area to move goods?

Dan said...

Good thoughts, Anonymous. A city with many bridges indeed! You might have something there. As for the matter of lowering the vehicle to the street, you are not alone in your opinion. Lots of very smart people agree with you. I am not one of them though, at least for now. In certain cultures or political systems it would work as you said. The problem is that such a system is not well suited for the economic realities of a capitalist, democratic system. For example, the ability to stop anywhere on route could only be used on track that doesn’t have enough vehicles to justify its construction in the first place. Meanwhile each vehicle must carry around the extra equipment, extra weight.

Obviously, we seem to get plenty of money for roadways that are empty much of the time, so there is a double standard at work… one that I don’t agree with… Nevertheless, early systems need to be only comprised of essentials that have a short payback period. I have further arguments, but I’ll save them for a future post. Like I say, there are many who see it your way, so probably a deeper discussion is in order.

Anonymous said...

An interesting article.

But a crazy an impossible scenario.

The total capacity on any major artery in a network would be the result of MANY stations at each end. Not just two.

So for a starter system, the maximum capacity is determined by the throughput at stations (and Masdar offers some insight on that) and for a fully developed system maximum capacity is determined by the throughput at main artery choke points.

It seems massively counter productive to try and have any discussion around massive station throughput when the main objective of PRT is point-to-point travel with many small stations.

In your example, each hotel and hospital building at one end and many stations downtown.

Befoer adding more than 4 berths to a station, find out where the passengers are coming from and create a new station

Dan said...

Dan the Blogger responds -
I guess I need to underline an essential point that I thought was understood. This example was never intended as anything like an ideal business plan. On the contrary, it was supposed to be used as an extreme case; An example that is well beyond where PRT generally ceases to be an effective strategy. OF COURSE PRT is supposed to have many smaller stations. We all know this. But (hopefully) we all also know that no city, in the REAL world, is going to come up with the funds for a complete network all at once. Locations that need only very small capacity are stations that are not on their radar, and certainly will be last in line for funding. The Squeaky wheel gets the grease. Insisting that PRT must be a network of small stations imposes a dogma on city decision makers that they don’t want or need, and I think this is partly why PRT has not gotten very far. I believe it is incumbent on system designers to provide as versatile a system as possible; Cities will come to understand the power of a network soon enough, if we ever get our foot in the door. I have not just designed some of the biggest stations, by the way, I have also designed some of the smallest - check out the one in post 150!