Escaping to the Movies

 

Here is a one way to deal with the troubling specter of people being trapped in hanging pods.  First I have to say, though, that such a thing could never happen;  (at least not with the SMART system being designed here!)  The vehicles all have robust battery backup, can go into reverse if the track is broken, and can be made to push or tow, and the individual vehicles are not tied to a central control that can create a cascading failure.  Furthermore, with only four moving parts in the drivetrain (those being the wheels) and manual override controls on board, the odds of ever needing  to evacuate  are infinitesimally small.  Nevertheless, there are those who might feel more comfortable with such a system in place anyway.  This is for them.

The support pole on the left has the system folded up and ready to deploy.  On the right it is ready for people to exit the vehicle.  The system should be able to be powered from the vehicle’s backup battery.  Not visible is the full winch and cable layout, which would work sort of like an automatic Venetian blind.  Unlike most designs in this blog, this is truly an “artist’s rendering.”  That is to say that it has not really been engineered with any degree of specificity.  Still, I think it demonstrates that a crude elevator can be folded up against the track and that the system can be pretty minimal.  Commodity  winches are widely available and inexpensive, and would be more than adequate for emergency use, so providing the system should not raise track costs significantly.  I would not expect they would be used on every pole or even every other pole, but rather, perhaps, every tenth one.  There would need to be a protocol for moving emptied vehicles out of the way, however.  

And speaking of only four moving parts, let me change subjects and give an update on my little motor project from a couple of posts ago.  Before going on my summer break, I did, finally, get it running, although not yet with any sophisticated stepper motor controllers.  So instead of ramping voltages smoothly, I am just dumbly turning electromagnets on an off.  But hey! - At least it works!  Also, my purpose here is to use this to build a working scale-model of a SMART style PRT system.  I am happy to report that the motor will work fine for that, including having sufficient  power for climbing vertically.  I have to admit, though, that it is very, very hard to build 3 more just like it, when I already have vastly improved designs in mind that I am dying to try!                

I also want announce the creation of a YouTube channel… It's the "openprtspecschannel"!  My sole video is of the motor in action, although I will tell you beforehand that if you just want to skip the technical stuff and just watch it run its demo program, just go to around the 5.5 minute mark.  It’s not a very professional presentation, with a couple of obvious mistakes, but for a spur of the moment, “first take” it will do just fine.  I just wish that I had explained a bit more about what hub motors are really, really good for, which is hollow-track PRT.  To summarize a couple of points that I failed to include:

Since PRT track should be thin as possible, there is precious little room for extra hardware.  Hub motors neatly solve this problem.  They are also (potentially) extremely efficient, having evolved as the most  competitive  method for powering solar race cars, for example.  The problem of trustworthy traction (that might seem to indicate a linear motor as a better choice) is not really an issue in an enclosed environment, not just because the track is dry, but also because it is easy to clamp onto the track’s interior surfaces in any emergency.  But there is more to it than that… Hub motors need not preclude linear motors.  There is no reason not to combine the two.  Indeed, there are potential advantages.  Since hub motors are direct-drive and essentially linear motors rapped into a circle, this common DNA would seem to indicate that a single control signal could easily synchronize both.  Such a hybrid could have enhanced acceleration and braking even with a smaller “flat spot” on the wheels. (traction area)  This means harder, rounder tires for more efficiency and durability.  Linear motors can react with permanent magnets, surfaces induced to be magnetic, or other electromagnets.  Face to face LIMs, for example, are essentially twice as strong.  Thus, for limited areas coming in and out of stations, a small, onboard LIM could pack a real punch combined with LIMs in the track.  Away from the station, it could play a role in centering the bogie, taking pressure off of centering guidance wheels, increasing their life.  It could even help steer. This is too complicated for early iterations, but it is nice to know that the option exists for some future time when people demand better and better performance. After all, with a cabin that is designed to cancel G forces, extremely rapid and nimble performance may come to be expected.  

Lastly, one problem with motors in general is heat dissipation.  This is especially true of LIMs, since they have no moving parts.  Consequently manufacturers include ports to pump water through them.  Hub motors, (at least “pancake style” ones) on the other hand, being thin but of large diameter, spread the heat out over a large area while using that large diameter to deliver great natural leverage.(torque)  It is extremely easy to vent such a motor to “pump” air past the coils while still having only a single moving part…the wheel itself.  And to reiterate one point from previous posts… Linear motors can have a problem with maintaining close proximity between the motor and the magnetized surface, especially when that space is between a vehicle and its track.  Rotary motors can inherently have rotors and stators nearly touching for minimum waste of magnetic flux.  

More  torque.  Direct drive.  More efficient.  Air cooled. Require NO extra space…  Easily integrated with supplemental linear motors.  This is why I think axial-flux, (pancake) style hub motors have a great future in PRT!

Anyway, get some popcorn and enjoy the movie!  Also, there are a few other axial flux and hub motor projects on YouTube, some quite impressive… Check ‘em out!

154> 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.

153> Fractals!

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.