Monday, January 24, 2011

116> Parkin' On the Hill...

This post is in response to comments made regarding the last one. In order to illustrate my points, I have used a modified version of the following picture, which I had originally intended to use in a different manner, so even though it is a bit off-topic, let me start with an explanation this illustration first.

This picture is the result of a design exercise, the object of which was to create the highest capacity station possible with the smallest footprint. In order to do this, I used elevators with curved doors, so that they can retract without needing much space in the walls. There are two of them, one for entering and one for exiting the station. This station is not “off-line,” but would rather be bypassed by a track that is not shown. Four cars can be loading while four are unloading, and (guessing a time of thirty seconds to get seated and on your way) the capacity of the station would be one car per 7.5 seconds, which works out to 480 vehicles per hour. It was designed to be ADA compliant, yet has a footprint of only about 50 square ft. One thing to think about is that if 8 of these stations where operating at capacity, the track they would be feeding would need sub-second headways to handle the passenger load. A station like this would be factory-built and delivered to the site in several pieces. Obviously the design is a bit misplaced in this setting, which isn’t exactly downtown, (so a footprint small enough for a crowded sidewalk isn’t really needed) but I had no other jpeg to “shop” the model into.

This leads me to the next picture, which shows a two-way variation of the same station. In this one, each elevator handles both arriving and departing passengers, with one elevator being for each direction. I drew this in response to alert reader Lars Endre, who suggested the possibility of using sloping track to capture the energy lost in deceleration. While this would be impractical for most PRT designs, it’s a concept that is well suited to self-leveling, hanging systems. The idea rests on the recognition that it takes a great deal of energy to get a vehicle up to speed and that it wastes a lot of kinetic energy to get it to stop. Parking atop a hill, so to speak, addresses both issues. This picture shows such an arrangement.

An alternative (frequently mentioned) approach to the problem is regenerative braking. As the vehicle slows, the momentum of the vehicle turns the wheels, which rotates the motor faster than it wants to go. This turns the motor into a generator and a brake at the same time, and the power is fed back into the track to be reused elsewhere. Sounds good when you say fast. I am not, personally, completely sure that this is an efficient process that is practical to exploit, what with electrical transmission losses, etc., especially with minor voltage supplementation in a DC system. 

Regenerative braking raises another fundamental question. How much braking do you want to do? After all, if the system is smart enough, it ought to have vehicles coasting more and braking less, right? The problem boils down to the need for speed. To some, it is assumed that assumed that PRT has a natural speed limit. Studies have shown that as speed increases, the safe spacing between vehicles must increase as well. Thus a system with a densely populated track going slower could move more people than one with faster, more widely spaced vehicles. The problem with those studies is a glaring fault in logic. It assumes that nothing can improve braking ability or crashworthiness of the vehicles. Fix that and you can both pack them tighter and go faster. But then we need brakes, and must deal with those mechanical inefficiencies. Consider the off ramp leading to a station. Making the split-off ultra gradual and giving a very long lead-up track is not very practical. 

Here is a different angle to show more track. While my first instinct was to think that raising the boarding area was a waste of materials, I soon realized that this cost could be offset by allowing shorter on/off ramps. Obviously this is more of an attractive option for fast, densely populated systems than for slower ones with few vehicles.

Another consideration is the “Umbrella Effect,” where overhead structures block the sky, a concern for landowners along the route. While this is less of a concern for minimalist track systems like I advocate, in a bi-directional station like the one shown there is still a lot of track up there, as can be seen. (Imagine the ULTra track four lanes wide!)  Long acceleration lanes represent additional visual obstruction. If raising the station can shorten these ramps, that would seem to be a plus for public acceptance as well as cost.  Even the station itself would appear somewhat less imposing by being higher, as more light would get in beneath it, and individual areas would remain shaded for less time. 

Astute reader Andrew F further pointed out that in tight turns, a sloping track could also be used to “bleed off” speed. (and give it back again after the turn) There are plenty of tight turns in a city environment, so this is something to consider. The negatives here are about ride quality, the way the system looks, the extra engineering, etc. Clearly, going very fast downtown would require a system that would be designed like a roller coaster, and I doubt we really want to go that far. On the other hand, in a system fast enough for commuting from the suburbs, there will always be the interface into the slower urban environment, just like freeway exits feeding downtown streets. Such an approach should certainly be in the toolbox. The case for using slopes to slow or speed a vehicle naturally arises, I believe, from the fact that it is so easy to do, considering that the track is raised anyway and the vehicles are designed to handle slopes and turns with minimal discomfort to the rider.


qt said...

And assuming regenerative braking works for this application, the two could be used together. Leave the track flat while regen-braking down from cruising speed. Let the car coast uphill for the last few dozen yards/meters to the station.

Regenerative braking becomes less effective (or so I've read) as the speed goes down. Roller-coaster geometry takes more space as the speed goes up (as was mentioned in the last post's comments). So you could use the regen-braking to shorten the uphill segment, while the uphill segment stores the car's kinetic energy more efficiently in the last hundred yards--and restores it MUCH more efficiently when the car starts out again.

(I've heard of truck drivers who have a greater-than-average concern for fuel efficiency who won't make a bathroom break at a rest area if it's at the bottom of a hill. They say they burn more fuel getting back up to speed than they would getting to the next rest area on that ridge east of here. I suspect they are using hyperbole (truckers are fond of that), but the point is there...)

Once again, more options. Always a good thing.

Rick said...

I agree with your analysis of the trade-off between regenerative braking and uphill coasting. The Toyota Prius gets about the same mileage in stop and go driving as in highway driving because of regenerative braking so it does work.

A PRT needs a battery backup to get to the next station in a power failure so with the right electronics the regenerative power could be fed into the battery.

I can see a "hybrid" system where the battery gets a trickle charge from the grid, the grid supplies power for constant speed operation and the battery provides for acceleration and braking.

Bengt Gustafsson said...

Some numbers regarding boarding times as measured by ULTra at Heathrow. Considerably shorter than 30 s:

Boarding 2.6 + 1.8n
Deboarding: 2 + 1.2n

where n i the number of passengers.

To this the doot times must of course be added, maybe 5s in an optimal system. This means that 10s cycle times are possible (a bus dwell time is typically on the order of 20 s, so it is not unreasonable for a small vehicle).

On the other hand, with inline berths the capacity goes down due to statistical effects of being held up by slower passengers in upstream vehicles.

Dan said...

Qt, I agree. Rick, I don’t really see the advantage in boosting from the battery when you’re already connected to the grid. I can imagine, perhaps, saving the charge to a capacitor to be used a few seconds later to “launch” the next vehicle. Anyway I wouldn’t want to tie the way the whole system works to the existence of a few regenerative stations. Bengt, thanks for the figures. Actually both upstream and downstream delays can cause multiple vehicle holdups with my design. One built-in delay is the time to advance the empties forward. Not separating the embarking and disembarking sections would semi-solve this, but this station is extremely minimal. The corridor to the vehicles is only 1.6m wide, so it could get crowded.

Rick said...

Dan, what I picture is each pod having a built-in battery (or super-capacitor) with enough capacity to get the pod to the next station at a slow speed with a reserve. This would require enough on board smarts and sensors to safely navigate to a station and avoid any hazard on the way without outside help. Only a damaged track or other obstruction would require the fire department to rescue people. The power from the grid could be out for a long time and with 5,000 pods it would be a major rescue effort.

The other thought is that with a battery on board the regenerative braking energy would never leave the pod but would be used to accelerate the pod. The power required to accelerate can be several times that required for constant speed operation. The power generated by braking would also be several times normal operating power.

Because the current is proportional to the power (at constant voltage) the electrical pickups could be rated for 1.5 (or some other reasonable safety factor) times the maximum current draw at constant top design speed.

The electronics could be designed to limit the current through the pickups and use battery power to aid climbing and acceleration. Regenerative braking power could be used to charge the batteries or excess power could be dumped to resisters to prevent over charging.

Regenerative braking can be very effective as the Prius has shown.

cmf-seattle said...

Regen braking on small-vehicle systems might be more trouble than it's worth (in newer installations, anyway). When GE's hybrid locomotive was announced, I thought it might be better to install energy-storage systems (sized to handle the current surge) at passenger stations, along with an appropriate length of overhead wire (pantograph on locomotive).


It is much cheaper to correct designs through analysis than after hardware is built. Analysis is hard, exacting work. Most engineers do not have sufficient mathematical background to do such work well and thus blunder along from one inadequate design to another. This “garage-shop” approach has initiated many designs, for example the bicycle and the automobile, but modern airplane and automotive design requires a great deal of analysis corroborated by experiment. Design of a truly cost-effective, high-performance transit system requires the best of modern engineering analysis. Perhaps this is the overall problem with PRT; to build a road, you just need a bulldozer/front loader.

Lars Endre said...

I got another argument against the elevated station here now; the power-failure situation where the pod's onboard power/auxiliary system is required to get You safely to a station, it would be better with flat tracks/stations. And surely, regen braking works, so on an electrical system like this, it would and should be introduced "anyway".

cmf-seattle makes the point that all systems better be well thought through before they are built; changes to the system later will be more costly. I totally agree (to the extent it doesn't completely stop development), and my expression of the same thing is this:
If you can build simpler; do. If you can build independence (f.ex. between pod and rail); do. If you can solve ANYTHING by design; do, and every need of computer controlled or electro/mechanical *something* that you can skip; hurray! (which was kinda the elevated station idea).

Great article, BTW. Thanks.

Andrew F said...

This is true. That station design is not up to code in much of the developed world. Stairs are a necessary safety feature.

Dan said...

Dan The Blogger Responds –

First of all, welcome back, cmfseattle! I hope your long absence was an indication of good (and not bad) fortune.

Rick, I think your idea of using batteries for acceleration shows a real problem with regenerative braking for PRT. There is no good way to store the energy that is harvested. In the Prius, the battery is huge. In the PRT vehicle, the battery is so small, there’s no way to add energy to it except to draw from it at every opportunity. This makes little sense to me because it is such a complicated (and probably less efficient) way to feed the motors compared to simply taking it off of the track, and would shorten the life of the battery.

I would also point out that stop-and-go driving is the mother lode of harvestable energy. That is totally different from the non-stop, uniform-as-possible objectives of PRT. There just isn’t much there. Finally, since the deceleration into the station probably is the best source for harvestable electricity, it seems to me that wayside capacitors are probably the easiest way to store most of it. After all, most larger motors use capacitors to help them start anyway.

Lars, I agree with your philosophy of simplification. We shouldn’t get too carried away with enthusiasm over niceties like harvesting each and every wasted watt. If we can do something simple and effective, fine. Other than that, that’s what design evolution is all about. As for stranding passengers, I am continuing to weigh a number of emergency evacuation options, and have no further comment at this time.

Andrew, good point… DUH!… It completely slipped my mind. Shows what happens when you are up to your elbows in something and don’t stop and stand back to see the big picture. What is worse is that the stairs will have a whole new set of safety regulations themselves such as width, rail height, baluster spacing, etc. So much for my tiny sidewalk footprint’

Finally, cmfseattle, about that quote… perhaps what we engage in here is a partial answer to his point. The only thing worse than not doing careful analysis is wasting resources by doing it on a whole lot of half-baked, unvetted ideas. Personally, I think we are building a pretty decent foundation.

Andrew F said...

The more I think about it, the more I have to conclude the stations should either be at ground level or within larger structures. Trying to make an economical, stand-alone elevated station seems like a bridge too far. It could be the second story of a strip mall, even, but a structure with enough other economic value to support stairs, elevators, etc. It need not be directly on the street after all.

Rick said...

Dan, a Prius weighs 2,800 lb and has a 100 lb battery. A PRT vehicle should weigh 1/4 of that and have a 25 lb battery. It is interesting that to extend it's life the Prius battery is kept between 45% & 75% of full charge by it's controller.

A motor controller with regenerative braking is not much more complex than one without. Brushless DC motor controllers used in machine tool axis drives have large resistors to absorb the energy rejected when the axis is decelerating and the motors you are considering require the same type of controller so the choice is between wasting the energy or using it.

Dan said...

Andrew, clearly I am largely in agreement, or I would not have included the swing-arm in the vehicle design. Its main function is to allow the track to descend steeply to allow street level stations without blocking adjacent streets and driveways. I have a feeling that there are a dozen or more good station designs of various heights that I haven’t explored yet. In the case of the design in the first picture, a staircase would be required at either end of the station. At least the narrow profile is maintained, if not the small footprint.

Rick, Clearly a decelerating vehicle will generate excess electricity and that energy can be applied to either the batteries or put back into the track. I’m sure there are ways to do this semi-efficiently that are so straight-forward that it would be almost silly not to employ them.

I would rather not get too specific, though, about battery weights, types or voltages at this point, but rather consider the matter more generically. It’s better practice to design from the “big picture” inward than the reverse. For example, would the batteries for a high-speed commuter system (or the rest of the vehicle, for that matter) be the same as for a system designed more for downtowns? What kind of track voltage would be best, and why? Will most stations end up being at grade or elevated? Will vehicles need to slow down to split off at an interchange? Any of these factors might influence battery/recharging system design. From a strictly hypothetical point of view, though, I guess I will add the following cautionary argument.

I think regenerative braking in PRT is directly comparable to another well-known low-RPM generating environment, direct drive wind turbines. It is well known that in light winds, wind turbines are essentially useless. Because power cubes as wind speed doubles, many owners of wind generators are unpleasantly surprised when they find out that their system, which works well with a 12 mph wind, generates next to nothing in a 5 mph wind. I think that the force of deceleration is comparable to the wind power in this instance. I would suggest that “hard” breaking from a fast speed is geometrically more productive than “soft” breaking at low speeds. Now if we assume that “coasting” (zero Gs) represents the equilibrium between adding and subtracting electrical charge, we see a situation where anything close to coasting makes power generation fall off precipitously. Unfortunately, that is exactly what PRT would be shooting for, from a comfort standpoint.

Andrew F said...

Dan, I'd imagine that you could comfortably apply much more braking force than friction/air resistance (from coasting), especially with all seated passengers. It seems to me that it would make sense to coast for some distance before the station but braking reasonably hard closer to the station. Relying on anything like coasting to a stop would decrease average speed significantly, and probably impact line speed as well. This is usually what car drivers do, at least. Seeing a red light ahead, they usually coast, then brake at a comfortable rate once they are closer. They don't brake uniformly over the whole distance.

Braking comfort usually has more to do with smoothness of deceleration than purely rate. I find subways and buses somewhat infuriating, especially when you're standing, because you'll occasionally get really hard jerks that can send unwary passengers flying. An audible warning in advance of braking (which ought to be possible in all but emergency circumstances) helps even more with passenger comfort.

All this said, I don't think regenerative braking will be a significant factor in system efficiency and may not even be worthwhile from an equipment cost perspective. After all, PRT should have much reduced stop-and-go characteristics compared to the 'city' conditions for automobile fuel efficiency tests.