The problem of wide corridors

One longstanding characteristic of public transit, is its linear nature.  Transit systems are generally (and ideally) organized in lines, on which some vehicle travels progressively from point A to B, and then in the reverse direction.  Not all such lines are geographically straight, of course, and many systems also feature loops with no discernible endpoints--but even in those cases, the vehicle makes progress towards some goal or direction, stopping along the way to let folks on or off.  Vehicles cannot be in more than one place at a time, nor do they (Amtrak's Empire Builder notwithstanding), split into two to serve different sets of destinations simultaneously.  Lines can branch, but you lose frequency on the branches--individual busses or trains running on the line can only serve one branch or the other, not both. (see Jarrett's excellent presentation for more on branching, and numerous other topics). 

But what happens when you have a wide corridor--a geographic area which is linear in shape, but where the key destinations don't lie in a convenient linear arrangement?

Examples

67 Map, courtesy of TriMet

Consider TriMet's 67 Jenkins/158th route, driven by our good buddy Al (who wants it known that he doesn't speak for TriMet, or his union, or anyone else but himself).   This route run between PCC Rock Creek and Beaverton Transit Center.  The primary routing is kind of zig-zag (the as-the-crow-flies direction is diagonal, but the streets for the most part are not), but that's close enough to linear for our goals.  However, the route contains two backtracking deviations, or as I prefer to call them, "cherries"--places where the bus leaves the main street, goes some distance to reach an important destination, turns around and backtracks, and then rejoins the primary service corridor.  One of these cherries, serving the Cornell Oaks business park, will be eliminated in September (a move praised by Jarrett).  The other, a shorter-stemmed cherry serving the Merlo/158th MAX station, remains in place. 

Or consider the proposed Barbur Boulevard corridor for a new MAX or BRT line.  Between downtown Portland and Tigard, there are several highly-important destinations (Tigard TC, Washington Square mall, PCC Sylvania, Barbur TC, Hillsdale, OHSU-Marquam Hill)--all of which, except for Barbur TC, aren't on Barbur.  A simple line parallel to the existing boulevard misses most of the action in the corridor--which is why various proposals for tunnels get floated about.  (I have no objection in principle to the proposal, but I seriously doubt that TriMet can afford it).

Or consider the Washington Square WES station.  Of course--there is no such thing; the nearest station to the mall is the Hall/Nimbus station (which isn't even located on Nimbus Avenue).  The mall is located about 2000' to the east, across a busy freeway and a major thoroughfare.  Connecting bus service is actually pretty good (between the 76 and 78, and the occasional 43, up to six busses per hour connect the Nimbus Avenue stop with the mall--that's more frequent than WES itself), but the transfer to the bus lines plying Hall Boulevard is a bit inconvenient, especially in bad weather.  WES was constrained to operate on the existing freight tracks, which lie on the opposite side of the freeway--but the mall is one of the most important destinations in the corridor. 


Wide corridors--sets of destinations which are clustered around some linear corridor but not sufficiently close enough to it (or across some barrier)--cause lots of problems for transit.  Serving them adequately requires diluting available service hours over greater numbers of route-miles--resulting in a net decrease in service quality.  In some cases, rapid transit lines may not be practical due to dispersed demand--and in the worst cases, the only sorts of services which are practical are inefficient "social service" routes.

What to do, what to do

Some possible solutions to wide corridors are discussed below.  These aren't solutions in the sense that they solve the fundamental problem; however they are different ways to provide service in a difficult situation.

Courtesy of thetransportpolitic.com

• Longer routes.  One way to serve the major destinations in a wide corridor is to lengthen the route.  The "cherry" mentioned above is one case; serpentine routes such as a proposal for Maryland's "corridor cities" are another example.  Either way, lengthening the route to cover the greater distances imposed by dispersed destinations effectively slows down the line, making it less attractive to riders.
• Splitting and branching.  If most of the trips are between destinations along the corridor and destinations elsewhere, branching may be an option.  Branching reduces frequency in the branches, of course, so doing so may also make the service less attractive; it makes travel between branches more difficult.   If the line requires fixed infrastructure, such infrastructure needs to be built on both branches.  One useful option here, though, is "open BRT"--the trunk can often be built to high busway standards, with the branches running in mixed traffic--if the branches are short, this arrangement often results in service of reasonable quality.
• Transferring.  One reason "grid" or "fishbone" arrangements are useful is that intersecting lines can be used to provide service to destinations which are slightly off-track, while keeping the trunk line straight and fast.  This depends a lot on the quality of the transfers, obviously--if getting the last mile requires a 20-minute wait on the side of a road in the rain, this is not an attractive option.  If, on the other hand, transfers can be timed and waiting occurs in a protected space, this is an excellent option.

Mid-levels escalator (HK), image courtesy Wikipedia

• Dedicated connecting service.  This is a subset of transferring, but the previous paragraph assumes a generic line that happens to pass close to a point of interest, but serves much else beyond.  A dedicated connecting service, on the other hand, provides point-to-point service between a station on the trunk line, and a given destination.  Such services may take the form of shuttle busses (such as the shuttles running between PCC-Sylvania and Barbur TC), a dedicated people mover (the Portland Aerial Tram functions in this fashion; even though its primary purpose is not connecting the Marquam Hill campus to the Portland Streetcar), or even a special-purpose transit line (such as the "Disneyland Subway" in Hong Kong).  With a dedicated service, there's ample room for creativity--the mode used might be outside the norm of services typically provided by the transit authority--and might not be funded by the transit authority anyways.  The dedicated service might even be passive--a skybridge or tunnel where people walk, for instance, but one which lets users avoid weather, obstacles, traffic, or difficult terrain. Generally, a destination has to be fairly major to justify this sort of infrastructure, but things like gondolas, shuttles, elevated walkways, public elevators and escalators, moving sidewalks, and such are all pressed into service to connect a transit line to the places people ultimately want to go.  (Many of these things additionally benefit pedestrians who aren't using the transit line as part of their trip).

Of course, as numerous writers cited above have pointed out, the best way to deal with this problem is to avoid it.  Good land-use planning can avoid widely-dispersed destinations--and result in land-use outcomes which are easier to provide service to.  The benefits accrue to well beyond transit--many other public goods, from police and fire protection to utilities, are cheaper and easier to provide if confined within a smaller space (It ought to be noted that automobiles, on the other hand, frequently benefit from dispersion--mainly due to their need for parking when not in use).  But there are many existing wide corridors which need service; and many popular corridors can be victimized by their own success--attracting development which widens the corridor as the closest lots become scarce and/or expensive.

Impedance matching and transit

This morning, the DHT takes a minor break from discussion of the Lake Oswego transit project, to emphasize a fundamental principle of transit design (one that certainly has relevance to Lake Oswego, and beyond).  Yours truly hold an MS in Electrical and Computer Engineering from Oregon State University, which implies that I know something about electricity and electronics.  (That said, I've spent the past fifteen since graduation doing software, which implies that I've probably forgotten most of it).  However, one important principle of electrical engineering, that of impedance matching, has significant relevance by analogy to transit.

Impedance is defined by Wikipedia as a quantity which "describes a measure of opposition to alternating current (AC)."  While I have some quibbles with that particular phrasing, they're off topic here on the DHT--the definition given is good enough for the purposes of this post.  Impedance can be broken down into two fundamental components: resistance (opposition to non-changing, or direct, current--always a positive number), and reactance (opposition to changes in current, which can be positive, negative, or zero).  Electrical circuits can be modified by a source (typically a voltage source, such as a battery or power supply), and a load (the device that does whatever work or performs whatever function is desired).  Both the source and the load have an impedance associated with them, and the behavior of the circuit depends on the impedance of both components.

Why impedance matters

In many applications, it is important that the impedance of the source and load be matched--a condition which occurs when the resistance of source and load are the same, and the reactance of source and load sums to zero.  Impedance matching is required for maximum transfer of power from source to load, and for minimizing "reflections" of the signal (which can disrupt communications).   The latter phenomenon is too complicated to do justice to in a post for laypersons; but the former can be be explained easily enough:  The power consumed in a circuit element is the product of the voltage drop across it, and the current which flows through it:  P = VI (I is used for current in the field of electronics--C is used for capacitance).   The current through a circuit element can be computed by dividing voltage over impedance: I = V/Z (Z = impedance; don't ask me why).   The total voltage of the source is distributed across the source and load impedances, V = VS + VL; where VS = VZS/(ZS + ZL) and VL = VZL/(ZS + ZL).  Thus, doing a bit of math produces the result that the power dissipated by the load is ZL (V/(ZS+ZL))²  Given that the source impedance ZS is often fixed, a bit of calculus shows that the load power is maximized when the load impedance ZL is set to match it. 


One problem with impedance matching is that while load power is maximized; so is source power, such circuits are only 50% efficient.  Efficiency can be computed by dividing load power over total power, under the assumption that only load power is used for doing useful work. To maximize efficiency, one deigns so that the load impedance as high as possible.  This limits the amount of power which can be delivered to the load, but in many cases that doesn't matter--if you have a 60W light bulb, it doesn't matter that the household circuit may be capable of delivering 2kW--you only need 60W to make the thing work.  Maximum efficiency is achieved by making the load impedance as high as possible relative to the source impedance.   This technique, impedance bridging, is generally only used in situations where reflections aren't an issue. 


On the other hand, if the load impedance is lower than the source impedance, to much power is wasted in the source or the interconnecting wires.  This is generally not a useful case, and in extreme cases is known as a "short circuit".

What of the source impedance itself? The source impedance of a power supply is in many ways, a figure of merit--lower is better.  A power supply with a lower source impedance will be able to deliver a higher maximum power for a given voltage level than a supply with a higher impedance; and will waste less power no matter what the load.  Unsurprisingly, designing power supplies with very low impedances is difficult and expensive. 

(EEs may note that I'm glossing over power supplies modeled as current sources--and they would be correct.  I'm glossing over lots of things...) 

What does all of this have to do with transit?

Good question. 

When designing a transit line, there are several important factors to consider:

• The nature of the route (including the vehicles): 
• The nature of the stops (distance between, amenities, platform height, etc)

A transit vehicle or system does two important things:  It stops to pick up or drop off passengers, and it moves to the next stop.   For both functions, minimization of time is required.  It's relative easy to come up with first-order figures of merit for both operations:


First, consider a transit vehicle which is deadheading on its route.  Here, the vehicle traverses the route, running under normal conditions and at normal speed--stopping at traffic lights, stop signs, and for obstacles in the road (other traffic, pedestrians, debris) as necessary--but does not stop to pick up passengers.   We could measure its velocity over the route, under various conditions, to come up with a number we'll call the deadheading velocity, VD.  Higher is better, obviously--and various things can contribute to a higher deadheading velocity:  higher-performance vehicles, a dedicated guideway (no interacting with other traffic), priority at intersections, etc.


Now consider the hypothetical case of a vehicle which traverses its route, stopping at stations and stops in the ordinary manner--but travelling instantaneously from one stop to the next:  when the doors close at one stop, the vehicle and its passengers are teleported instantly to the next needed stop.  We add in a per-stop penalty for to account for acceleration and decelation as well. Assume that each stop is serviced normally--if little old ladies need to fumble through their purse to find exact change, that time is counted.  Were we to sum up all the stop times (averaged over numerous runs), and divide them into the length of the route, we would come up with a number I'll call the service velocity, VS. 


Now, let's invert the two parameters, VD and VS.  Science doesn't presently have a good term for the inverse of velocity, so I'll coin one:  lethargy, or L (LS, LD).  The lethargy of something is the amount of time it takes to cover a distance, divided by the distance.  Why do we use lethargy?  Because, lethargy is additive.  The total lethargy is simply the service lethargy plus the deadheading lethargy.  (One can invert the total lethargy to get the total velocity, or an approximation thereof--keep in mind, this is a crude model).  If it isn't obvious already; lower is better.



How lethargic is good?



What values of lethargy are good?  Bad?  Typical?  First, lets consider some typical LD values for various modes of transportation:

• Jet air travel:  < 0.12 (>500MPH)
• Turbofan air travel, true high speed rail: 0.2 - 0.3 (200-300 MPH)
• Second-tier high-speed rail : 0.3 - 0.5 (120-200 MPH)
• Amtrak, rural freeway: 0.7 - 0.9 (65-85 MPH)
• Urban freeway (no congestion), grade-separated metro: 0.8 - 1.2 (50-75 MPH)
• Rural highway: 1.1 - 1.3 (45 - 55 MPH)
  
• Urban expressway with stoplights, i.e OR224: 1.5-1.7 (35-40 MPH)
• Median-running light rail:  1.7 - 2.1 (28-33 MPH)
• Urban boulevard: 1.8 - 2.2 (27-32 MPH)
• Urban arterial: 2.4 - 3.0 (20-25 MPH)
• Light rail, traffic in downtown grid: 2.4 - 3.0 (20-25MPH)
• Residential streets: >3.0 (<20MPH)

Now, LS.

• Point-to-point auto travel: < 0.1 
• Point-to-point commuter bus/rail, >10 mile trip:  < 0.5 (assuming 2.5 mins for loading and unloading)
• Point-to-point air travel: <300 mile trip (40 mins to load, 20 mins to unload plane): >0.2
• Point-to-point air travel: <300-600 mile trip: 0.1 - 0.2
• Point-to-point air travel, >600 miles: < 0.1
• Corridor commuter rail/express bus (such as WES):  0.1 - 0.3
• True-metro rapid transit, 1-2 mile stop spacing, 30-40 second dwell:  0.33 - 0.5
• Transit, 0.6-1 mile spacing, 30 second dwell: 0.5 - 0.8
• Transit, 0.4 - 0.6 mile spacing, 20 second dwell: 0.8 - 1.3
• Transit, 0.2 - 0.4 mile spacing (1000-2000 feet), 15 second dwell: 0.6 - 1.2
• Transit, 750 - 1000 feet, 15 second dwell (i.e. Streetcar):    1.2 - 1.6
• Transit: 500-750 feet, 10 second dwell: 1.1 - 1.5

For a given service type, by adding the corresponding lethargies for the route type and the stop spacing, you get a good estimate of the overall lethargy--and the overall speed.


What lethargies do riders generally expect or encounter?  Values less than 1.5 are generally rare, but here are some "typical" values:

• Point-to-point commuter rail: 1.5
• Corridor commuter rail, i.e. Sounder or WES:  1.8-2.2 (WES is 2.4; due to shorter-than-typical stop spacing and tracks not rated for higher-speed operation).
  
• Point-to-point highway-running express bus: 1.8-2.0 (i.e. C-Tran 199)
• Corridor express bus: 2.2 - 2.6 (C-Tran 105)
• "True" metro: 1.7 - 2.2
• Dedicated-guideway light rail:  2.0 - 2.8:
• Dedicated guideway BRT, limited stop, no signal priority:  2.5 - 3.0 (LA Orange Line)
  
• Median-running light rail (i.e. yellow line): 2.8 - 3.2
• Suburban highway bus: 3.0 - 3.5 (the 33 and 35 are both in this range)
• Rapid streetcar:  2.8 - 3.5
• Proposed Lake Oswego streetcar, LO-PSU:  ~3.5 
  
• Downtown light rail: 3.5 - 4.0
• Urban boulevard local bus (ie TriMet 9): 3.5-4.0
• Local bus: 5.0 - 10.0
  
• Portland Streetcar downtown:  ~8.0
  

Excluding express and commuter services, a common cutoff for rapid transit is a lethargy of about 3.0 (an average speed of 20MPH).  High-quality rapid transit can do 2.0 or better; medium-quality, about 2.5.   Frequent stop (non-express) bus service running in mixed traffic on ordinary streets has a hard-time doing better than 3.0, and mixed-traffic streetcar is unsurprisingly, very slow.


What does this all mean?

The reason I use lethargy, in addition to the fact that it's easy to compute with--is that it's analogous to the electrical property of impedance discussed in the first section.  Furthermore, deadheading lethargy is analogous to source impedance, and service lethargy is analogous to load impedance, in the following ways:

• Power consumed in the load, and time spent picking up and dropping off passengers, is useful.  Whether a high or a low value is good or bad depends on the application--commuter rail (and point-to-point transport) have very low service lethargies, as the bulk of the time is spent in transit--but don't serve very many people.  Local bus service, on the other hand, has a very high service lethargy--it stops in lots of places--but this limits its effective speed.
• Deadheading lethargy, like source impedance, is a figure of merit--the lower, the better.  And like source impedance, making it lower costs money.  Time spent in transit is generally time wasted, just as power consumed in the source is wasted energy.  
• Most importantly, it is useful to match lethargies, just as it is useful in electonics to match impedance.  Building expensive transit infrastructure, but running services with frequent stop spacing on top of it, does not lead to better service, at least as far as this analysis is concerned.  (There may be other reasons--reliability, capacity, sex appeal, whatever, to do so; all of these things are outside the scope of this post).  
• On the other side of the coin, running limited stop service in mixed traffic is useful--express bus and commuter rail being two examples--but these services generally have low impact.
• Finally, like impedance, lethargy is logarithmic in its impact.  There's a  bigger difference between lethargies of 2 and 3, then between lethargies of 5 and 7, for instance.  This logarithmic nature makes higher-performance lines difficult and expensive to build; it's far too easy to build too many stops on a line to garner greater political support, sabotaging its technical merit in the process.  (MAX downtown suffers from this problem to some extent--that said, MAX was designed to provide local service through downtown; not to be an efficient means for crosstown trips).

While we wait for the USA-England world cup match to begin...

A quick quiz:

Which of these urban transport vehicles is a cable car, and which is a tram?

(Images courtesy of Wikipedia)

Chances are, if you live in an English-speaking country which drives on the right--particularly the United States, you'll be familiar with the San Francisco Cable Cars, and identify the image on the left as such.  You may be less familiar with the Portland Aerial Tram--unless you live in Portland, it isn't exactly a well-known landmark--but the term "tram", to Yankee ears, refers to any number of miscellaneous (and relatively uncommon) people-movers, including the custom-built inter-terminal railways found at airports, the centipede-like parking lot shuttles found at Disneyland, and to cable-hauled aerial gondola systems like found between Marquam Hill and South Waterfront.  Likewise, Americans generally use the term cable car to refer to cable-hauled railways. 

If you live in merry ol' blighty, on the other hand, a "tram" is what in the US is called a "streetcar"--a passenger railway or railcar which runs in or near the street (or which is capable of doing so), regardless of haulage.  And given that cable-hauled railways are actually pretty rare; the term "cable car" generally refers to cable-hauled aerial systems in the UK (see the aforementioned article for a good breakdown of the terminology).  Thus--a Brit may well describe the Portland Aerial Tram as a "cable car", and the San Francisco Cable Cars as "trams".  And he'd be correct, insofar as his dialect of English is concerned...

Confused?  So am I. 

Now enough silly linguistic arguments.  It's almost time for soccer.  I mean football....