Capacity of Personal Rapid Transit Systems

When everything is coming your way, you´re in the wrong lane!

his web-page deals with the traffic capacity of the beam network in inner-city areas. These areas are usually characterized by many high-rise buildings close together, and this makes for a high concentration of people. While one of the big points with PRT-systems is that the web should be as fine-meshed as is motivated, rather than collecting traffic onto big trunk lines, we have found that trunks are necessary in order to off-load the local lines.		Capacity of Personal Rapid Transit Systems Capacity of the Trunk Lines One-way or two-way Traffic? The Intersections A finer mesh

1. Capacity of Personal Rapid Transit Systems

. Edward Anderson, Ph.D., P.E. has gathered some interesting observations on a paper called "The Capacity of a Personal Rapid Transit System". The observations made in this paper are the result of practical observations, made by himself and by his students. These observations reveal that people coming out after major sports events, or at the end of the working day from a big work site, etc. do not come all at once. They are subjected to various bottlenecks, and because people are aware of these bottlenecks, they generally take it easy and await their turn. This has a significant impact on the required capacity of a public transit system during times when they have to swallow a lot of people, such as after sports events at big arenas. Typically, people enter through turnstills and leave parking lots, etc. at the rate of one person every 3 to 5 seconds. This rate is of course proportional to the number of turnstills and gates, but if there are too many gates from a parking lot, for instance, then there will be bottlenecks somewhere else; in the street, at the nearest intersection, etc.

Figure 1:1

Thus, when calculating for a maximum capacity of a PRT or GRT station, it is not necessary to take the raw figures of the expected onrush of people at a certain time. If one calculates with the bottlenecks that apply in each case, one will usually find that the transportation capacity need is not that demanding, at a particular station. Mr. Anderson makes the assumption that 50% of all travelers in a given city area will use the transit system we are looking at. Let's be more ambitious! Let's assume that we have a city area whose streets are closed to public transport and private cars, and there are no trams or subways! Then presumably 90% of all people will use "our" PRT system, since it's the only means of transport available. The remaining 10% will walk, use a bike or take a cab. Apart from this difference, we will adopt mr. Anderson's reasoning, and see where we end up!

Based on available statistics (from USA), the number of individual peak-hour trips are about 0.3 times the population in a given urban area. When calculating in this manner, one has to figure the number of people that actually are within this area at this time; not only residents but also those who work there. Consider, then, a square network of streets, with a PRT network along some of these streets, having east-west and north-south traffic lines as shown in the illustration above (figure 1:1). The lines discussed here will each be in alternating directions, spaced about 800 meters apart, which is a typical distance between major streets in western cities (a typical city block is between 100 and 200 meters in length, so we make the very rough estimate that about every 5:th street is a "major" street). The stations should be evenly spaced, and having a spacing that will place every location within 400 meters of a station. The stations are also assumed to be at the midpoints of each pair of intersections (see figure 1:1, which only depicts major streets. The red lines are "our" PRT-system, with stations in the middle between each intersection).

hus, a pedestrian should have, at the most, 800 + 400 meters = 1200 meters to walk to the station of his/her choice (since he/she in most cases cannot walk in a straight line), considering that each station only carries traffic in one of four available directions. This means, of course, that the person should not have to stand at the optimum position (marked with O in figure 1:2, but rather at the most awkward positon (marked with A). We agree that 1200 meters is a rather long distance to walk for most people; two-way traffic would considerably ease up this situation. But let´s continue this line of reasoning. Mr. Anderson then goes on to say: - "Let the population density be 12 000 persons/sq-mile, which is high for most U.S. auto-oriented cities." This figure is indeed so high that it's reasonable to assume that both residents and those who work in the area during the day are included. Then, within each one of the half-square-mile squares between beam traffic lines, constituting a "major" city block of 800 * 800 meters there would be 12 000 / 4 = 3 000 people and, during the busiest hour, this would generate 0.3 * 3000 = 900 individual trips/hour. One could, (for ease of understanding) divide each "major" city block into 4 400 * 400 m squares, as shown in figure 1:3. Each of these four squares would be served by a station, but each such station also has to serve a 400 * 400 m square in the adjoining city block.		Thus, each station would have to handle half of a "major" city block, giving an average station-flow requirement of 900/2 = 450 individual trips/hour, assuming that we have an even distribution of people between stations. As we stated above, 90% of these people will be assumed to travel with the beam traffic system, which comes to 0.9 * 450 = 405 persons per hour and station, which is slightly less than 7 persons per minute! This is also an idealized situation, insofar as we assume that equally many people want to travel in each of the four directions. If some suburbs are larger than others, this will of course not hold true; the traffic demand in those four travel directions would then be uneven. Let us assume that 205 of those 405 people each opt for travel in an individual beamcar, while the other 200 share a car (it could be that some will travel with a larger, scheduled car, that runs after a timetable, but we will leave that option out in these calculations). Then, each station would "generate" 205 + 200/2 = 305 cars an hour, which is about 5 beamcars per minute. If (for instance) there are 10 stations after each other along a street, before the local line meets up with a trunk line, then this particular street would feed the trunk with 10 * 5 = 50 cars a minute. And there are more streets with more local lines to feed this same trunk.	Figure 1:2 Figure 1:3

n this particular example the network could be rather strained during rush hour. And, if we are to base our statistics on the observed pattern of 1.25 persons riding in an average motorcar (at least in USA and Northern Europe), those 405 people per hour at each station during rush hour would generate closer to 405/1.25 = 324 beamcars per hour, rather than 305. If a beamcar spends 1 minute on the average at a berth, each station in our example would require at least 7 berths for parallel loading, and enough beamspace for buffering of at least 15 cars. As shown below, this buffering would probably have to be done on beams, reserved for the purpose, between the stations. There should be shunts to trunk line beams after about every 15 stations or so, to take the load off the thru-lines, passing along the streets. We could thus get 4 parallel beams in each direction:

one beam for stops, one for the buffering of beamcars, one for thru-traffic within city blocks and one trunk line to off-load the thru-traffic line with cars that are going farther away (and at a higher speed). This might seem like over-doing it a bit, but we must not forget about resiliency in the network; If something happens to one or all beams along a street to put them out of action, there should be enough capacity on the parallel beams of nearby streets to handle the extra load. As shown in the illustrations further down, the trunk lines could very well be at right angles to the streets (and beams) they off-load, but then they would be parallel to the beams in those streets. But a well-designed network could handle this demand, and a population "density" of 12 000 people/sq-mile would only apply to the central downtown of a big city, or to a major sports arena.

2. Capacity of the Trunk Lines

et's take a look at the trunk lines, using the example above. From the table regarding traffic capacity for various decelleration speeds we can assume a traffic handling capacity of about 50 vehicles per minute for each beam, corresponding to T=1.2 seconds between vehicles. So, if each group of 10 stations feed the trunk with 40 cars a minute during peak traffic times, we will have to add almost one new beam to the trunk line for each such "feeder" group of local lines. As has been stated elsewhere, as the beam network expands its capacity for a given urban area, the emphasis should be put on making a fine mesh of it, rather than collecting the traffic into high-capacity trunk lines. But in this example we have a dense city core, where a finer mesh does not fill any real purpose. Why? Because we already have beams in practically every street, in our example. We can´t get a finer mesh than that, also considering that the city might not want beams in every street, for one reason or another. So; we have to interweave the local lines with trunklines to handle the big traffic flow. The 2 schematic illustrations at right show 2 ways of doing this. One way is to let the local lines for each group of 10 stations join trunk lines that goes at a 90 degree angle to the local lines, as shown in figure 2:1. The advantage with this arrangement is that the trunks could then also facilitate traffic between nearby parallel local lines.

figure 2:1 figure 2:2

figure 2:3	figure 2:2 above has the trunk lines running in parallel along the local lines. For every new group of 10 stations that is added from the local line onto the trunk line, another beam is added to the trunk line. These trunk lines could then meet up with trunks going in the transverse direction, as is shown at the bottom of figure 2:2. figure 2:4

figure 2:5	If we were to look at the cross-sectional views (from figure 2:2 above) as these trunk beams are added, it could look like the views A through D shown here. One could extend the supporting poles up to 3 tiers (maybe even more). Considering that the beams would be crossing each others at intersections, several tiers would be required anyhow. As can be seen from views A and C, the trunk beams are preferably put on the highest tiers.	The local beam is on the same tier as the beam for the stations, as these two beams need cross-connections with one another before and after each station. The beam for the stations is indicated by the vertical arrow, showing that on this beam the cars will stop at the stations. When there is such a short distance between stations as in our example, there is no point in having the station-beam join the local thru-traffic beam altogether. The station beam will in all probability branch out at each station, in order to handle passengers in parallel, and it might be necessary to add more of these beams to make room for car buffers, i.e. for beamcars waiting to take on passengers (or cargo).

Since the beams in our example will follow major city streets, these can be assumed to be rather broad, i.e. at least 2 lanes in each direction + broad sidewalks. Then, one could arrange for the beams to go above the streets, as shown in views B and D. A combination arrangement, like the one shown in view E, is not indicated in figure 2:2, but this allows for 2 beams for buffering cars, and 2 beams for allowing the cars to stop without impeding thru-traffic. This flexibility is important during the expansion phase of the network. Thus, cars could stop in the streets for passenger exchange, before proper stations have been built, or "proper" stations might not be needed in some places. It should also be pointed out here that the progressive addition of trunklines, as shown in figure 2:2, were used for illustrative purposes. In reality, those trunks will follow the whole street (or row of stations along the local lines) since these local lines will in all likelihood go from one set of transverse trunk lines to the next. The parallel trunk lines will thus only serve to off-load the local lines with such traffic which is not going to stop along the stretch of network that this particular local line serves.

figure 2:6 figure 2:7

3. One-way or Two-way Traffic?

t is clear from mr. Ewdward Anderson's scheme; one-way traffic in alternate major streets, that he calculates with one physical conduit as being sufficient to handle traffic demands. SwedeTrack's figures (with our ambitions of handling 90% of all travelers) show that several parallel conduits will be necessary. Why not then have two-way traffic in these streets, providing for shorter average walking distances to the nearest station that carry traffic in the desired direction? That would be the obvious solution. If the beams have to be erected, why not then use them in a more versatile manner? The requirement for trunk beams in each direction would be halved, to one trunk beam for each 30 stations instead of 15. For two-way traffic, the required number of beams would be the same. But there is one more attraction to this scheme; flexibility. Some trunk beams could be used in different directions at different times during the day, as the traffic flow changes. Thus, it could look like the very schematic figure 3:1. The thick lines are trunk beams, the blue (vertical) lines buffering beams. The reader will have to imagine the cross-connections between beams between all stations, the shunts to the transverse trunk beams at top and bottom and also the corresponding beams running across the figure (call it the east-west direction, if you like). A closer view is shown in figure 3:2, where the 2-way traffic is better seen. Opposite every block there is a station (indicated with red rectangles in figure 3:2), which in turn could consist of several berths. These berths could stretch along for most of the block, making it possible to have a berth within 60 yards or so, no matter where you happen to be in the downtown. It should be remembered, though, that this applies to the downtown areas where traffic demands requires these many beams. In not-so-dense cores of, for instance, satellite cities, where demand is lower, mr. Anderson's one-way traffic scheme would be the ideal solution.

figure 3:1 figure 3:2

A typical street scene could look like view F. If the middle trunk beam is used in alternating directions as need be, there should rarely have to be any need for more than 3 trunk beams. If you think that this view would be too intruding on the city landscape, you should consider that this altogether replaces today's 2-3 lane traffic (in each direction) with its noise, pollution and out-crowding of pedestrians! Just imagine the silence as compared to the racket of motor vehicles, and street shops who can keep their doors open in warm weather, which is virtually impossible today, because of the traffic in the street outside.

figure 3:3

4. The Intersections

The observant reader will no doubt have noticed that the views A, C, E and F above might not work well if there are crossing beams at major street corners. They would work if at least one of the following conditions is met: The crossing beams are on a still higher level, with platforms above the streets, as shown in figure 4:1. The crossing beams are put in tunnels The crossing beams are at ground level, allowing the cars to travel like trams The crossing beams have their closest stations so far away that the beams could dip under one another. The last point is not problematic, since the beams need to have frequent shunts between each other anyhow (vertically, in this case, see "sloping beams").

figure 4:1 Otherwise, the straightforward solutions would of course be to put the beams on 2 different levels, as shown in view G. The beams at the higher level would have to dip down at the stations, so that the beamcars could reach the ground.

5. A Finer Mesh

This page would not be complete if we did not consider the alternative of erecting beams in practically every street. Why? Because the purpose of streets is to allow traffic, and the beam traffic system can replace most forms of street-bound traffic. The more streets that can be covered by beams, the less would be the need for vehicles on the ground. And city streets can once again be dominated by pedestrians. In the example above, we assumed that only major streets would have beams and stations, giving the average traveler a walking distance of 400 meters on average. We also assumed that there are about 5 blocks between parallel major streets. Putting bi-directional or single beams in every street and a station at every block would result in people having considerably less walking distance; they would in most cases find a station right outside their door. This would result in smaller stations, harboring one or two vehicles at a time, and it would off-load the stations in the main streets, enabling those stations to be reduced in size as well. As a further bonus, there would be less beams in the main streets, and less crowding on those beams serving the stations. The load on the trunks would be reduced, because more travel within the city could take place on the local beams. This is because all the additional beams would of course help to off-load each other and could thus swallow more traffic. On the down-side, this alternative would require considerably more beams. figure 5:2 Look at figure 5:2 above. This is how it would look if we decided to avoid crossing beams altogether in the smaller streets. A car travelling from A to B would have to go in a rather roundabout way to reach its destination. This solution could work if the traffic volume is not too big. Avoiding multi-level crossings would make the construction easier and cheaper, and would of course also reduce the intrusion in the city neighborhood. A closer view of what it would look like is shown below (figure 5:3). figure 5:3 Stations would have to be placed on sidings, so the network would resemble figure 5:4 at right. Stations are indicated by yellow squares, insofar as each such square is a berth that only have space for 1 car at a time. Thus, a station consists of one or more berths. The main problem with this arrangement is that people need some time to get in and out of the beamcars, so in reality there would have to be several berths in a row for each station, as mentioned above. This is shown in figure 5:5 at right. This arrangement means, however, that the cars will be in each other´s way. The solution to that problem is parallel berths, as is shown in figure 5:6 at right. But that, in turn, requires broader streets. Not in order to accomodate the beamcars, but to make room for the beam sidings with their berths. To complete the overall picture, one could let most of the trunks travel in tunnels to keep them out of view until they reach the outskirts of the downtown area. This would have the added advantage of avoiding the awkward multi-tier beam crossings at street intersections (as in figure 4:1 above).

figure 5:4 figure 5:5 figure 5:6