One
thing concerns me about the typical vision of a PRT system is the idea that should
consist entirely of a network of one-way loops that would be expanded by adding
new loops contiguously. This seems to me to be an oversimplification, and generally
not the most efficient design in terms of system cost or travel time. Yet even bi-directional
routing can be thought of as a loop, of sorts – just one that has been squeezed
along its length. So how could the paradigm of one-way loops be lacking?
First
of all, let’s take an idealized example where the density of potential riders
is completely even and the track forms a perfect grid of squares. (round the
block loops) Clearly there will be a bias towards higher ridership on routes crossing
the middle than at the outer edges. So what do we do? Is the middle subject to
wait times or are the outer routes paid for, but underutilized? Add to this the
fact that the middle will probably have more potential riders anyway, and you
can see that the problem is just that much worse.
Beyond
that, the assumption of an ever-expanding network of contiguous loops tends to
ignore the uneven distribution of important destinations. Although cities have
a central business district that needs to be the heart of a PRT system, after
that there are seemingly no rules for what should come next. A spider web
design is better than the grid, since the converging radial routes enable a
somewhat denser concentration toward the middle. But cities don’t grow evenly
and the transportation bottlenecks can be far from downtown, an inconvenient fact
that would-be PRT providers will surely downplay. After all, there is plenty to
be done downtown, so why worry that far ahead? I say, “Inconvenient” because really dealing
with it increases the complexity of a system immensely. In my opinion the
solution will have to include some combination of multiple speeds, multiple
vehicles sizes, and multiple, parallel tracks- like there are multiple lanes on
a freeway. Anything less, and the
system will be one that can only solve some of the problem in some of the
situations, and that fact may be baked-in by the design and therefore forever
unfixable.
If there is only one speed, all track must be routed without
any sharp turns if the system is to be fast enough to be useful for anything
more than very short trips. This means acquiring right-of-way on nearly every
corner or bypassing needed, but troublesome routes. Then there is the matter of
multiple vehicle sizes. Here I am referring to GRT. Certain routes, say to an
airport , stadium or “park&ride” lot might benefit from a larger shuttle-type
service rather than only individual smaller vehicles. This would help with the
rush hour demand for routes that many passengers share in common, without
requiring extra track or vehicles just for a few hours each day. The third
option, multiple parallel tracks, is also for this situation. One of the great things about PRT is
that it can be designed to have very inexpensive track, which makes such
possibilities more palatable. I think following the familiar highway model,
where there is both a high-speed express and a more local feeder aspect might
be particularly advantageous. Such an investment paves the way for future loops
along the way, and could often be done using existing highway easements.
In either of these last two cases it is assumed that there
are enough destinations along the way (or at either end) to justify a
PRT-compatible track rather than say, an ordinary bus. Having GRT sharing the
track reduces what would otherwise be a requirement for more parallel tracks, but
parallel tracks, if spread apart by a few blocks, would provide enhanced access
all along the way. Like I said, there should be some combination, if at all
possible, of these three methods. This may complicate the system design, but it
makes the system more versatile and therefore ultimately a more compelling
value.
So how are we to determine the relative merits of the
various systems and routing schemes? I think there are probably some
mathematical formulas that describe the general problem and give some ballpark
ratios and other guidelines that might be useful as a starting point. Such
formulas seem to follow the general principles of fractals, something that
occurred to me when Nathan Koren ttp://www.podcar.org/blogs/nathan-koren/, in
this excellent two-part (similarly themed) post, used a leaf as an example of a
transportation system.
Imagine a growing town building new roads outward into
surrounding countryside. Along each new road are natural “sweet spots” to develop
housing, warehousing, retail, etc. Any closer, and land is too expensive. Any
farther out, and the commute is too far. Maximizing the usefulness of the new
road and access to these areas can be accomplished with simple branching. Now
you have twice as many sites with the same travel time without needing separate
roads. Branch the branches and now you have four. Branch once more and you have
eight. Indeed, radially emanating roads must diverge if they are to access any
reasonable portion of the ever widening land mass anyway.
This follows the rules of a type of fractal geometry known
as the Lindenmayer system, (L-system) which is seen thoughout biology and is
efficient for movement of blood, plant nutrients, etc. The math for the above
example is simple. Go a distance, split, go half as far, split, go half as far,
split, etc. (I cut the "trunk" to save space) Add a bit of randomness and you can create forms which look like
photographs from a botany book.
Want to live on a cul de sac? This “H tree” (left) gives
everyone the piece and quiet of their own dead end, equidistant from the main
road.
To the right is what is called a quadric cross, which represents
a three-way split at right angles.
Here is a different kind of
fractal geometry at work: Let’s consider, for a moment, the merchant. Here we
have the same desire for cheap property, but it is coupled with the need for
exposure to customers. Clearly the intersections formed by branching roads are particularly
advantagous in this regard. But another plus would be the presence of other
businesses, to help draw customers. This too, can be described in mathematical
terms with more fractal geometry, this time with what is called a “Diffusion-limited
aggregation.” (DLA) Here, particles (businesses) randomly migrate from a source,
but not too far, only to plant themselves on an edge (2D) or surface. (3D) This is not unlike coral growth, and can be
seen in satellite views of cities, especially aspects like pavement coverage
vs. green areas. In three dimensions, constrained by city blocks, an effect much
like crystal formation is seen in the growth of groups of multistory buildings.
Again, these similarities are not merely coincidental. They are the result of
similar natural, measurable forces.
What is interesting about the combination of
DLA and L-system effects in city growth is that together they generate satellite
communities. This formation is easy to observe by anyone who takes a farm road
out of town. It usually starts with a gas station/convenience store at a rural
intersection. Soon an eatery or an auto repair garage follows. As more
businesses join the group, land values rise, creating a climate for land
speculation and further development. Much, much later the resultant communities
create a traffic nightmare for the host city by interfering with the radial
flow of vehicles during rush hour. In the typical spider web roadway
configuration the radial strands that serve the central area are inherently at
odds with the concentric routing that serves traffic between neighboring
outlying communities. This creates pockets of traffic congestion that are far
from downtown but are still sorely in need of something like PRT. The classic
remedy has been to build a freeway with overpasses over the main crossing
roads, cutting the outlying communities in half.
These fractals only go so far in
describing the problem facing people tasked with designing PRT routing, because
of the subject that I brought up first, which is loops. After all, notably
absent in the earlier discussion about a “sweet spot” was the obvious way to
get the most bang for the buck. That is to have the branches loop back upon
themselves. Fractal forms can include loops as well, as in the leaf below. Note
the classic fractal multi-scale self-similarity in the tendency towards
branching at right angles.
Below is a fractal of loops
representing growth along an east/west corridor. I have included some secondary
development, (shown in red) representing the value of shortcuts. The next step
would be to connect the outlying areas directly to form an outer loop.
The “rules” outlined above do more
than help explain the uneven geographical distribution of potential PRT
traffic. They also illustrate the different capacity requirements for the track
itself. I drew the L-system tree with separate lines on the “trunk” to
illustrate the simple fact that there simply cannot be equal traffic between it
and the branches. The quadric cross example also shows the relative traffic
increases (line thickness) toward the center. Either the branches are at a
fraction of capacity or the trunk is overburdened. As I stated earlier, the
idea of simply handling peak loads with massively parallel loops is iffy at
best. But multiple lane trunk lines or GRT have drawbacks as well.
The conventional thinking used to
be that starter downtown circulator loops could be added to until eventually
there is a network that fulfills the total needs of the covered areas. There is
still some truth to this, but it certainly isn’t the whole story. Cutbacks in
government transportation spending have forced us to examine any and all
inefficiencies, including any underutilized track or vehicles. In the end we
will probably end up using some combination of “all-of-the-above.” I am not
sure how useful fractal modeling can actually be in practice, but the subject
certainly seems worth pondering. Surely there is a fractal form whose shape is
the result of a mathematical modeling of various forces that shape our cities,
and therefore our transportation needs. One thing is for sure. We shouldn’t be
surprised when we find that the most cost effective and expandable PRT solutions
mimic nature more than a checkerboard, or use many of the same techniques that
have proved effective in moving people via our current network of roads.
