Saturday, April 14, 2012

140> Piping Hot Ideas

Recently I was reminded by one reader just how many posts I have written, and just how difficult it is to use this site as a resource. Blogs are just like that. The new builds on, but buries, the old. If you come in late, you just don’t know what is going on. Yes, I (ug!) need to update the table of contents and index… Anyway today I am going to go back to the very foundation of the designs found on all of those back pages, the primary design distinction that tends to define and distinguish one PRT system from another… the track.     

The right track is everything. Think of it like a pipe for moving people. After all, our whole way of life is a study in the progress of learning to pipe goods and services with ever greater efficiency. Look at email vs. treemail! Gas pipelines! And, of course, there is the many mile journey of the water coming out of your garden hose and into your flowerbed.  Back in Roman times, huge structures were erected to transport water because it had to be kept flowing gradually downhill. Once pressurized pipes and pumps were introduced, however, water could, for the first time, be efficiently moved anywhere in any direction. Our street system bears some resemblance to those ancient aqueducts, for reasons that contain elements of the same logic. Our vehicles are optimized for relatively level travel, abrupt turns require slow speeds, and of course, gravity is what keeps everything on track. In fact, it is a little appreciated fact that our city streets generally ARE aqueducts, insofar as they are carefully pitched to carry any rainwater away from homes and buildings, without ponding, to the nearest storm sewer. Conversely, highways, being designed expressly for speed, bear more resemblance to pipes or tubes. They are not referred to as traffic “arteries” for nothing! Unfortunately highways have severe limitations that mean that this analogy can only go so far. They are, frankly, huge. They rely on good weather and gravity and use acres of land for a simple turn. Pipes, on the other hand, can go anywhere – up, down, over and under. Their containment means higher speeds are possible and their compact form disguises the surprisingly high volume that a continuous flow can represent over time.  There are places, in some countries, where the water truck still comes down the street so that people can come out and fill their containers. In rural areas, people still rely on fuel trucks stopping by. In the transit analogy this is like buses or light rail letting off passengers. It’s a cumbersome, stop and go world. Piping is so much better.

Futurists have been playing around with the people-pipe idea forever. Anyone out there old enough to remember the Jetsons? The facts on the ground are, however, that physical pipe for humans isn’t really the most practical way to go. It’s too large, and a main point of piping is to economically extend the reach of a resource into all required areas. So the challenge is, then, to devise a system that can move people as though they are being piped, yet be small and flexible enough to be easily extendable into a large network, the way other ”piped” resources are.

Before going any farther, one interesting point about moving people. Oddly, we have little knowledge of how fast this can actually be done. Those familiar with the designs in these pages know that the PRT vehicles herein are specifically designed to eliminate sideways and front-to-back G-forces. For example, a passenger’s beverage, set down, will not spill, much like a bucket of water tied to a rope can be swung in circles, even up-side-down, without spilling a drop. This is contrary to (and better than) our finest, most advanced vehicles, be they luxury cars or fighter jets. There are, however, unavoidable variations in ordinary, vertically oriented gravity and these can cause discomfort. I recall that when I was a child, elevators would give me that weird feeling in the gut. I’m not sure, but I suspect that, over time, the acceleration/deceleration control in elevators has been greatly improved - carefully calibrated to make the effect almost unnoticeable while getting you to your floor just as fast or faster. In any case, doing this in 3D is a brand new field. Nobody has actually tried moving people from here to there as fast as possible, without making them feel yanked around. I predict that the combination of simulated free-hanging and precisely calibrated acceleration and deceleration will prove to be surprisingly effective in “piping people” comfortably. PRT has historically been assumed to have vehicles all moving at the same speed. It was a matter of control. These days, and even more so in the future, PRT vehicles may be programmed to act more autonomously - to be opportunistic - to go as fast as passenger comfort will allow. After all, that is what would happen in fluid dynamics. The Bernoulli principle applied to transit!
There is a lot more to say on this subject, such as the possible dizzying effect of looking out the windows, but that is for a different post. Let’s get back to designing the “pipe”.    

So what is the most minimalistic form factor that can hold a vehicle the way pipe walls hold in liquid? In theory, a simple pair of rails is all that it takes. Anyone who has seen a rollercoaster in action can attest to the fact that two rails can rapidly direct and redirect people through 3D space. (Remember, rollercoasters are purposely designed to throw you around, so I sort of hate to use them as an example) Anyway, though, it shows that two rails will work.

The notion of only two rails is a bit deceptive, however. The fact is that holding those two rails in proper orientation requires the lion’s share of the structure. So in actuality, it really doesn’t matter. Two, three, five rails or more…what matters is the overall weight vs. the span vs. factors like ease of construction and material cost. The big question for track designers becomes the tradeoff between many closely spaced supports vs. fewer, but with more massive and costly beams or trusses instead.

This brings up the question of what people will accept visually. Many current systems create a profound canopy effect, particularly where the track splits off to enter a station. If the system is to be two-way the problem is greater still. This effect weighs against the four-wheels-on-the-bottom paradigm seen on most vehicles. That said, the preferred profile for beams or trusses for making long horizontal spans is tall and narrow, not short and wide.  

But there is one other factor. There is the tradeoff between more vibration and noise but long wheel life, on one hand, and a quieter, smoother ride with less wheel life on the other. An obvious example is wheels made of steel or hard plastic vs. rubber tires. This conflict arises from, and is proportional to, speed. At high enough speeds hard wheels are very loud and soft wheels wear out very quickly, as racing fans well know.  The best remedy is to have larger wheels, which, of course, have more surface area. So this, too, gets weighed into the debate about PRT track profile for any fast, wheeled system.

A few decades ago, PRT pioneer Dr. J. Edward Anderson concluded that the best compromise for his single level, but raised, system was a truss about  waist high and about two thirds of that wide. He would use the structure to enclose and support the rails. I have drawn the same conclusion, as far as general dimensions go. This really is sort of a “Goldilocks” compromise. It gives enough interior space for the larger wheels that high speeds with semisoft wheels require and it encloses any noise anyway. (Not to mention weather-proofing the running surfaces!) It allows spanning lengths sufficient to cross at least six lanes of traffic, (Two lanes, each way, plus a turning lane is a very common city intersection size.) It has close to the ideal proportions of width to height.

I have physically placed similarly sized objects, such as large trash cans at a distance to simulate how big the track would look from the ground, and I am satisfied that these dimensions will be found acceptable almost universally, especially if they can contain otherwise unsightly utility wires and improve street lighting in the process. Also, with a fully 3D system the track can be set as high as need be.

So that, for all you new or occasional readers out there, is a brief explanation of the thinking behind the track that you will see on these pages. What I propose is essentially a bogie within a slotted tube that pulls along a vehicle in such a way as to whisk people from anywhere to anywhere faster but more comfortably than any of us have so far experienced. In full 3D. It would, of course, have all of the system traffic management normally associated with PRT and enjoy the benefits of in-vehicle, rather than track-based switching. The bogies use wheels that turn themselves without any additional moving parts and so are exceedingly efficient, especially since they use track-supplied electricity. Oh, and one other thing… It’s fast. It’ll take you from here to there in no time…without snapping your head around!  


Asko K. said...

>carefully calibrated to make the effect almost unnoticeable while getting you to your floor just as fast or faster. In any case, doing this in 3D is a brand new field.

It's rather simple, really, and all around us in street and rail transport. "Clotoid" or Euler spiral transitions from straight to circular curve smoothly. The maths is somewhat complicated - integral calculations - but doable for computers.

Roads and rails use this in 3D I presume, at least in 2D (know for sure). It can be applied to other things s.a. change of horizontal speed (i.e. don't apply 0.2G right from the start but grow from 0 to 0.2, then keep there, and again the same when lessening the acceleration).

I made these recently for my simulator, though simulating just with straight-to-curve would be enough.

Dan said...

Dan the Blogger responds! - I guess my wording was misleading, Asko. Of course you are quite right, as far as simply changing the velocity of objects in the midst of complex curves. I was referring specifically to vehicles that are designed to cancel or semi-cancel those G-forces by leaning into them. There are almost no examples to draw from. Motorcycles lean into turns, but what vehicles lean forward to accelerate? The Segway and unicycles come to mind, but that’s really a lot of human intervention. And what about leaning backward as you’re slowing down? The closest thing I can come up with is a perfect landing in a hang-glider, where you lift the nose up and stall, just above the ground. Again, there is human involvement.

The possibilities of unbalanced or changing-balance loads, as well as sudden extreme wind gusts, have forced me at adopt a simulated, rather than actual, free-hanging system. This means that the degree of lean in any direction will be programmable. I have noticed that highways do not bank sufficiently to cancel all sideways forces. Is this on purpose? Is it more comfortable to “feel” the turn, at least partially? Would it be the same for leaning into acceleration or deceleration? If so, by how much?

I rode a ski-lift once, and as I recall it had some fancy way to slow the seats down as they rounded the boarding area. Once you got in, though, it was Whoosh! The seats accelerated and climbed at once, and since we were hanging, all G forces went to holding us firmly in our seats. I wish my memory of it was better, I don’t even recall getting off at the top. Anyway, that is probably as close as anyone will come to experiencing what I am talking about, until I get around to building one of these things. It is my guess that going from a standstill, at ground level, to full speed (at “cruising” altitude) for merging can be done extremely quickly, smoothly, and comfortably… Although nothing short of human tests, I believe, will really sort out the most comfortable algorithm. That’s what I mean by a new field… the human response to this 3D G-force mitigation strategy, including tilting the vehicle forward and backward,as well as side to side.

Asko K. said...

Amusement park device makers do this all the time. They would know exactly what people feel as comfortable (boring) and what now. :) May be worth to ask.

Asko K. said...

now -> not :)

Andrew F said...

The toughest thing to address would be the negative Gs associated with descending from the main guideway to stations at ground level. This can only be done so quickly without causing nausea.

I've started to wonder whether we might need two 'lanes', one for higher speed through traffic and one for lower speed local traffic. If you think about the length of guideway required for acceleration/deceleration lanes for stations, the only way to get tolerable Gs (for the non-thrill seeking public) and frequent stations (every few hundred meters/yards) is to have relatively low speed (say, 40 - 50 km/h or 25 - 30 mph) guideways with station siding, with an 'express' lane that can travel at 100+ km/h. Having this two-layer network also means you can allow for tighter turns on the slower portion.

This is something like the highway 401 we have in Toronto, which has 'collector' lanes and 'express' lanes. You can only move between the two sets of lanes every three or four exits. This helps to manage the traffic and lane-changes you might otherwise have associated with a 12 - 16 lane highway.

Dan said...

Well, all I can say is that all of this underlines my reasons for trying to design a system that isn't particularly rule-bound. I really would rather let the system be adaptable as possible, and let future operators and users tweak it as they see fit. Anyway, thanks, guys... Time for "DTB" to leave this McDonalds and head back to the cabin, where I have been redoing almost every aspect of the bogie. I'm flying back to civilization on Weds.

Rick said...

Dan, what Asko is getting at is a method to minimize the Jerk when going from a straight section to a curved section at a constant velocity. Jerk is the 3rd derivative of position with respect to time (Jerk[ft/sec^3] = d_a/d_t just as Acceleration[ft/sec^2] = d_v/d_t & Velocity[ft/sec] = d_s/d_t). The curve can be in a horizontal plane, a vertical plane or a combination.

Because F = M*a, a sudden change in acceleration (Jerk) is the same as a sudden change in force. On a person this sudden change may not give the rider time to adjust their muscles to the new load. An example is an elevator that does not have Jerk control: A 150 lb person in an elevator that accelerates at 0.2G would suddenly weigh 180 lb and may not be able to adjust to the extra 30 lb in time to prevent a fall.

Going from a straight section to a constant radius curve at constant velocity results in very high Jerk. Mathematically the Jerk is infinite but because of flexibility in the structure the change in acceleration is spread out over a short period of time. Because we do not want to slow down going into a curve the track should be built with Euler transition curves. A free hanging system will oscillate if the acc/dec transitions are too high- that is, if the side force goes from 0.0 to max in less than ¼ pendulum period. Control Jerk and other disturbances can easily be controlled with simple dampers (shock absorbers). I don’t think an active control of tilt is necessary.

Leaning into G-forces is what people do instinctively as long as the forces grow gradually enough. Straight line acc/dec should have Jerk limiting, i.e. linear increasing/decreasing acceleration set to x.x ft/sec^3 while curves should have Euler transition curves.

High values of Jerk in a mechanical system are analogous to a step input to an electrical circuit and will result in oscillation or ringing. Because of the ringing the peak stresses in parts of the system can be much higher than that due to the force required for constant acceleration.

Dan said...

Rick, that’s a splendid explanation of what Asko was getting at. I will point out, though, that I am talking about accelerometer (level/gravity detector) based servo controls that would react in real time, to simulate free-hanging, except with some dampening to prevent, for example, swinging back and forth.
To use your example of entering a radius less than gradually, the (hanging) passenger compartment would tend to keep going straight instead of jerking. This would then be followed by a pretty heavy bank as the vehicle gets “whipped” around the curve. The example does indeed show that the transitions that Asko spoke of apply here, just not in the same way as a supported vehicle. One extremely important question I have been pondering is the switch to a parallel track. I say “extremely important” because it would happen anytime one exited a faster lane, such as to go to an off-line station. The scenario would be a quick right, then an immediate left. In theory, a hanging vehicle with dampened self-banking could smooth out a pretty jerky transition. This would reduce the amount of track, it’s visual profile, etc. It also has relevance in the likely scenario of a system being “ramped-up,” speed-wise, as the system gets more traffic, over time.

This makes me think about considerations on the ground. Those jerk-free turns are going to be hard to accomplish in some cityscapes… after all, the right-of-way will often be tight. One final thought… I wonder… to make a sharp right angle turn where there is little ability to do anything gradually, with a hanging vehicle, would it make sense to start the banking process, somewhat unnaturally, BEFORE the turn, so that the vehicle doesn’t swing up so violently? This would involve yet-to-be-invented solutions for anticipating such turns.

Dan said...
This comment has been removed by the author.
ItsEric said...

Optimal pod positioning for accel, decel, and turns is very similar to aircraft autopilot operations and many advanced amusement park rides. PRT pods should only need two servos (10 degrees both directions) with one handling side to side leaning and one handling forward/rearward leaning.

Aircraft autopilot use a combination of air sensing & gyroscopic sensing to correct for outside disturbances and brings the aircraft back to proper altitude, direction, & speed. They can also handle waypoints where they change one or more of their aircraft’s speed, direction, & altitude all the while doing it in a manner that is comfortable to the passengers.

Amusement park rides likely use timing or location markers to adjust positioning as needed.

A PRT system could install a guide way turn indicator just before the turn (say a ¼ second, 20 feet, 6 meters, etc) to notify the pod of the turn and to begin any leaning deemed needed for it. A typical smart phone has enough computational power to handle these tasks and would reduce the network bandwidth down by having onboard processing.

Andrew F said...

Off-topic comment with regard to news that Google is actively seeking to license to or partner with automotive companies to deploy its robocar technology. I'm wondering just how rapid the adoption of this technology will be, and how it affects the economics of PRT. I think there's a real risk that robocars won't be worse-enough than PRT to justify the infrastructure investment except in niches (campus/airport circulators, transit in dense areas with a lot of pedestrian cross-traffic, etc.)

I prefer the idea of PRT, because it will likely be able to offer average speeds that beat even very mature robocar technology because of inherent limitations of rubber on asphalt, cross traffic and pedestrians.

Dan said...

Hi Eric – I wonder where you get the 10 degrees from. Staying within easements is going to create a bunch of hairpin turns that will slow the whole system down, and 10 degrees won’t help out much. I know that airlines are very conservative, although I’m pretty sure I’ve been on commercial planes that did 12-15 to get into a landing pattern. I flew on a private jet once and I can tell you that they sure don’t stay within parameters anything like that. They climb fast to save fuel.

One thing, though, that is worth mentioning is that the 10 degrees (or whatever it is) will sometimes be in the context of a bogie that is greatly more out of level than that, so mechanically speaking, at least when it comes to forward and backward, we need a full 90 degree range. Anyway, I will be a bit surprised if 11 or 12 degrees (or more) aren’t found to be acceptable and advantageous in some situations, particularly starting and stopping. Oh, and I must say I’ve been watching the evolution of QR codes (for vehicle-readable “signs”) with great interest. I proposed using visible optics for position sensing back in post 94, and actually designed a similar square box. They must have been around back then, but I had never heard of them. And PS.. Thanks for putting some life into those old threads. I’m hoping to get caught up enough, one of these days, to give your comments some thoughtful replies!

Andrew, those Google cars will get just as stuck in traffic as the rest of us. Hopefully they’ll come around and see they’ve written some great next-gen PRT control software!